AP Physics 1 Quiz: Vectors And Motion In Two Dimensions

What this quiz covers

This quiz focuses on Vectors And Motion In Two Dimensions, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. It has both horizontal and vertical acceleration components.
2. It has only horizontal acceleration because it is moving rightward.
3. It has only vertical acceleration downward. (correct answer)
4. Its acceleration points along its velocity vector at all times.

Explanation: This question tests understanding of acceleration components in projectile motion. When a ball is thrown and only gravity acts (ignoring air resistance), the acceleration is purely vertical and downward at 9.8 m/s². There is no horizontal acceleration component regardless of the ball's motion direction. The fact that the ball moves rightward doesn't create horizontal acceleration - it just means the ball has horizontal velocity. Choice D incorrectly suggests acceleration follows velocity direction, but gravity always acts downward regardless of motion direction. In projectile motion, acceleration is always vertical (downward) while velocity can have both components.

Question 2

1. The horizontal velocity component.
2. The vertical velocity component. (correct answer)
3. The horizontal acceleration component.
4. Neither velocity component changes; only position changes.

Explanation: This question tests which motion components change during horizontal projectile motion. When a rock is launched horizontally from a cliff, it starts with only horizontal velocity and zero vertical velocity. Gravity acts downward, providing constant vertical acceleration that changes the vertical velocity component from zero to increasingly negative (downward) values. The horizontal velocity component remains constant because there's no horizontal force or acceleration. Choice A incorrectly suggests horizontal velocity changes, but without horizontal forces, this component stays constant. In projectile motion, gravity only affects vertical motion - horizontal motion continues unchanged.

Question 3

1. It stays constant because the acceleration is perpendicular to it. (correct answer)
2. It increases because the puck’s total speed increases.
3. It decreases because some velocity is “used” to accelerate north.
4. It reverses direction once the northward velocity exceeds the eastward velocity.

Explanation: This question examines how perpendicular acceleration affects velocity components. The puck has eastward velocity and experiences northward acceleration from the fan. Since the acceleration is perpendicular to the eastward velocity, it cannot change that velocity component - it only adds a northward velocity component. The eastward velocity stays constant because no force acts in the east-west direction on the frictionless surface. Choice C incorrectly suggests that velocity is somehow "used up" or redistributed, but velocity components are independent. When analyzing 2D motion, remember that acceleration in one direction only changes velocity in that same direction.

Question 4

1. The horizontal velocity components are equal at both points. (correct answer)
2. The vertical velocity components are equal at both points.
3. The total speeds must be different because time has passed.
4. The horizontal velocity is smaller on the way down due to gravity.

Explanation: This question assesses symmetry in projectile motion at equal heights. Independent perpendicular components allow horizontal velocity to stay constant throughout the trajectory. Vertical velocity changes sign but has the same magnitude at symmetric points on ascent and descent. Therefore, at points of equal height, horizontal velocities are identical, while vertical velocities are equal in magnitude but opposite in direction. Choice B incorrectly states vertical velocities are equal, overlooking the sign change between up and down. A transferable approach is to exploit trajectory symmetry for equal-height points, equating speeds and horizontal components while noting vertical direction differences.

Question 5

1. The horizontal velocity $v_x$
2. The vertical acceleration $a_y$
3. The vertical velocity $v_y$ (correct answer)
4. The total acceleration magnitude

Explanation: This question evaluates understanding of velocity and acceleration at key points in projectile trajectories. The independence of perpendicular components means horizontal motion proceeds with constant velocity, unaffected by vertical changes. Vertical motion experiences constant acceleration due to gravity, causing the vertical velocity to change linearly from positive to negative. At the trajectory's peak, the vertical velocity (v_y) momentarily becomes zero, while horizontal velocity (v_x) remains unchanged. Choice A distracts by suggesting horizontal velocity is zero, which might stem from misunderstanding that the peak halts all motion. A useful strategy for projectile problems is to sketch the trajectory and note that vertical velocity is zero at the maximum height, aiding in component analysis.

Question 6

1. It decreases because gravity pulls the puck downward.
2. It increases because the puck speeds up as it falls.
3. It remains constant because there is no horizontal acceleration. (correct answer)
4. It becomes zero at the instant the puck reaches its lowest point.

Explanation: This question examines the behavior of horizontal speed in free fall after horizontal launch. Independence of motion components ensures that vertical acceleration from gravity does not alter horizontal velocity. With no horizontal forces like friction or air resistance, the horizontal speed remains constant throughout the flight. The puck's vertical speed increases, but this is separate from the unchanging horizontal component. Choice B misleads by suggesting horizontal speed increases due to overall speedup, ignoring that total speed changes from vertical contributions alone. For analyzing motion off edges, remember to treat horizontal velocity as constant and use it only for range calculations.

Question 7

1. half the time, because it moves faster horizontally.
2. the same time, because vertical motion is independent of horizontal motion. (correct answer)
3. twice the time, because it travels twice as far.
4. a longer time, because greater horizontal speed reduces downward acceleration.

Explanation: This question tests the concept of time of flight in projectile motion with varying horizontal speeds. Perpendicular components of motion are independent, so horizontal velocity does not influence vertical displacement or time. Both balls start with zero vertical velocity and fall under the same gravitational acceleration, leading to identical vertical motion equations. Thus, the time to reach the ground depends solely on the height and gravity, resulting in the same fall time for both. Choice D incorrectly claims greater horizontal speed reduces downward acceleration, confusing independence with coupled motions. When comparing projectiles, focus on vertical parameters for time-related questions to avoid mixing components.

Question 8

1. Both $a_x$ and $a_y$ are nonzero and constant.
2. $a_x=0$ and $a_y$ is constant downward. (correct answer)
3. $a_x$ increases as $a_y$ increases during the fall.
4. $a_x$ is constant and $a_y=0$ after it leaves the table.

Explanation: This question assesses the skill of analyzing acceleration components in projectile motion. In two-dimensional motion, the horizontal and vertical components are independent due to the perpendicular nature of the axes. Without air resistance, no horizontal forces act on the ball, so its horizontal acceleration (a_x) is zero. Vertically, gravity provides a constant downward acceleration (a_y = -g), affecting only the vertical motion. Choice A is a common distractor, incorrectly assuming both components have nonzero acceleration, perhaps confusing projectile motion with motion on an incline. To solve similar problems, always resolve motion into independent horizontal and vertical components and apply constant acceleration equations separately.

Question 9

1. Behind the cart, because vertical motion reduces horizontal speed.
2. Directly above the launch point, because vertical and horizontal motions cancel.
3. Ahead of the cart, because gravity increases horizontal speed.
4. Horizontally aligned with the cart, because both keep the same horizontal velocity. (correct answer)

Explanation: This question investigates relative motion in combined horizontal and vertical projections. Independence of components means the ball retains the cart's horizontal velocity upon launch. Gravity affects only the vertical motion, causing the ball to rise and fall symmetrically. Both ball and cart share the same constant horizontal speed, so their horizontal positions align when the ball returns to launch height. Choice A suggests the ball lands behind, mistakenly thinking vertical motion slows horizontal progress. In moving-frame problems, switch to the ground frame to equate horizontal velocities and predict coincident positions.

Question 10

1. The vertical motion determines the horizontal motion because gravity sets the trajectory.
2. The horizontal motion determines the vertical motion because forward speed creates lift.
3. The motions are independent, with constant horizontal velocity and uniformly accelerated vertical motion. (correct answer)
4. The motions must be treated as a single one-dimensional motion along the curved path.

Explanation: This question evaluates the relationship between horizontal and vertical motions in projectiles. The components in perpendicular directions are independent, with no causal link between them. Horizontal motion proceeds at constant velocity, while vertical motion is accelerated by gravity. This separation explains the parabolic trajectory without needing to combine them into one dimension. Choice D is a distractor that suggests treating the curved path as one-dimensional, which complicates analysis unnecessarily. Always decompose into x and y components and solve separately for efficient problem-solving.

Question 11

1. Both components are zero at the top because it momentarily stops.
2. The vertical component is zero, while the horizontal component is nonzero. (correct answer)
3. The horizontal component is zero, while the vertical component is nonzero.
4. The vertical component is maximum in magnitude at the top.

Explanation: This question examines velocity components at the peak of projectile motion. The perpendicular components of motion are independent in projectiles, allowing separate analysis. At the highest point, the vertical velocity is zero because that's where it changes direction, but horizontal velocity remains constant. There is no horizontal acceleration to change the forward speed. Choice A is a distractor, falsely claiming both components are zero, confusing the momentary vertical stop with total velocity. A transferable strategy is to sketch velocity vectors and their components at key points like the apex to visualize independence.

Question 12

1. It must be zero because the ball is moving downward.
2. It must be smaller than before because vertical motion “uses up” speed.
3. It is unchanged from its initial horizontal component (constant). (correct answer)
4. It increases because gravity adds speed in the direction of motion.

Explanation: This question investigates horizontal velocity persistence in projectile motion. Independence of perpendicular components ensures that vertical changes do not alter horizontal velocity. The horizontal velocity remains constant throughout the flight, regardless of vertical direction changes. Even when vertical velocity is downward, horizontal stays the same as initial. Choice B is a distractor, implying vertical motion diminishes horizontal speed, which violates independence. To solve, note that without horizontal forces, velocity in that direction is constant—use this to predict components at any time.

Question 13

1. The horizontal component only.
2. The vertical component only. (correct answer)
3. Both horizontal and vertical components.
4. Neither component; only the total velocity is zero.

Explanation: This question focuses on velocity components at the peak of projectile motion. At the highest point of a projectile's path, the vertical velocity component must be zero - this is what defines the highest point. The projectile stops moving upward (positive vertical velocity) and is about to start moving downward (negative vertical velocity), so it must pass through zero. However, the horizontal velocity component remains constant throughout the flight since there's no horizontal acceleration. Choice D incorrectly suggests that total velocity is zero, but only the vertical component is zero while horizontal motion continues. Remember that at the peak, projectiles still have horizontal velocity.

Question 14

1. Horizontal acceleration is $0$ and vertical acceleration is $-g$. (correct answer)
2. Horizontal acceleration is $-g\cos30^\circ$ and vertical acceleration is $-g\sin30^\circ$.
3. Horizontal acceleration is $-g$ and vertical acceleration is $0$.
4. Both accelerations are $-g$ because gravity affects the whole velocity.

Explanation: This question tests understanding of acceleration components in projectile motion. Once a projectile is in flight with no air resistance, the only force acting is gravity, which acts vertically downward. This means the horizontal acceleration is always zero (no horizontal forces), while the vertical acceleration is always -g (taking upward as positive). These accelerations remain constant throughout the flight regardless of the projectile's velocity or position. The initial angle affects only the initial velocity components, not the accelerations during flight. Choice B incorrectly attempts to decompose gravity along the initial velocity direction, but gravity always acts vertically regardless of motion direction. To analyze projectile motion correctly, always remember that acceleration components depend on forces, not on velocity directions.

Question 15

1. The horizontal velocity decreases, causing the ball to “turn” downward.
2. Gravity provides a constant downward acceleration that changes only the vertical component of velocity. (correct answer)
3. The vertical velocity causes a horizontal acceleration through coupling of components.
4. The total speed must remain constant, so the velocity rotates downward.

Explanation: This question tests understanding of independence of motion components in two dimensions. A projectile's path curves because gravity provides a constant downward acceleration that continuously changes the vertical velocity component while leaving the horizontal component unchanged. This constant vertical acceleration causes the initially upward vertical velocity to decrease, become zero, then increase downward, creating the characteristic parabolic path. The distractor D incorrectly suggests that total speed must remain constant, implying some conservation that doesn't exist in projectile motion. To understand projectile paths, recognize that constant vertical acceleration combined with constant horizontal velocity produces a parabola, with the curve resulting from the changing vertical component.

Question 16

1. Only the vertical (downward) component. (correct answer)
2. Only the horizontal component in the direction of motion.
3. Both horizontal and vertical components because the ball moves diagonally.
4. Neither component because acceleration is zero after the kick.

Explanation: This question tests understanding of independence of perpendicular motion components by identifying acceleration components. The soccer ball is kicked northeast (having both horizontal components) but the only force during flight is gravity, which acts vertically downward. Since acceleration equals net force divided by mass, and gravity is the only force, the acceleration is purely vertical (downward) with magnitude g. The horizontal components of velocity remain constant because there is no horizontal acceleration. Choice C incorrectly assumes that diagonal motion requires diagonal acceleration, confusing velocity direction with acceleration direction. The strategy is to identify all forces acting on the object - in projectile motion without air resistance, only gravity acts, providing only vertical acceleration.

Question 17

1. Both components are zero because the ball stops briefly.
2. The vertical component is zero, but the horizontal component is nonzero. (correct answer)
3. The horizontal component is zero, but the vertical component is nonzero.
4. Both components are nonzero because the ball is still moving.

Explanation: This question tests understanding of independence of perpendicular motion components at the trajectory's highest point. At the peak of a parabolic path, the vertical velocity component becomes zero (the ball stops rising and is about to start falling). However, the horizontal velocity component remains unchanged from its initial value because no horizontal forces act on the ball. The ball continues moving horizontally even at the instant when vertical motion reverses. Choice A incorrectly assumes that zero vertical velocity means the ball stops completely, failing to recognize that horizontal motion continues independently. The strategy is to analyze each component separately at special points - at the peak, only the vertical component that was fighting gravity becomes zero.

Question 18

1. The launched ball takes longer because horizontal motion reduces vertical acceleration.
2. The dropped ball takes longer because it has no horizontal velocity.
3. They take the same time because vertical motion is independent of horizontal motion. (correct answer)
4. They take the same time only if the launched ball’s horizontal speed is small.

Explanation: This question tests understanding of independence of perpendicular motion components by comparing vertical fall times. Both balls start at the same height with zero initial vertical velocity - the dropped ball has no horizontal motion while the launched ball has horizontal velocity. Since vertical motion is independent of horizontal motion, both balls experience the same downward acceleration due to gravity regardless of their horizontal velocities. The time to fall depends only on the vertical motion parameters: initial height, initial vertical velocity (zero for both), and gravitational acceleration. Choice A incorrectly suggests that horizontal motion somehow reduces vertical acceleration, which contradicts the independence principle. The strategy is to recognize that when analyzing fall time, only vertical motion matters - horizontal velocity is irrelevant to how long it takes to fall.

Question 19

1. The horizontal velocity decreases because the ball is speeding up vertically.
2. The horizontal velocity remains constant while the vertical velocity changes. (correct answer)
3. Both horizontal and vertical velocities remain constant after leaving the table.
4. The vertical velocity remains zero because there is no initial vertical motion.

Explanation: This question tests understanding of independence of perpendicular motion components in projectile motion. When a ball rolls off a table, it maintains its horizontal velocity from the table's surface while simultaneously beginning to accelerate downward due to gravity. The key principle is that horizontal and vertical motions are independent - gravity only affects vertical motion, not horizontal motion. Without air resistance, there is no horizontal force acting on the ball, so its horizontal velocity remains constant throughout the flight. Choice A incorrectly suggests that vertical acceleration somehow reduces horizontal velocity, which violates the independence principle. The strategy is to analyze forces separately in each direction: no horizontal force means constant horizontal velocity, while downward gravitational force means increasing downward velocity.

Question 20

1. It is smaller than at launch because gravity reduces all components of velocity.
2. It is zero because the ball is back at the starting height.
3. It is the same as at launch because there is no horizontal acceleration. (correct answer)
4. It is larger than at launch because the ball has gained speed while falling.

Explanation: This question examines velocity components when a projectile returns to launch height. When a ball is tossed upward and forward, it has both vertical and horizontal velocity components initially. Throughout the flight, the horizontal velocity remains constant (no horizontal acceleration), while the vertical velocity changes due to gravity. When the ball returns to launch height, its vertical speed equals the initial vertical speed but in the opposite direction (now downward instead of upward). The horizontal velocity, however, remains exactly as it was at launch since no horizontal forces acted on it. Choice A incorrectly assumes gravity affects horizontal velocity, but gravity acts only vertically. Remember that in projectile motion, horizontal velocity never changes.