Displacement, Velocity, and Acceleration - AP Physics C: Mechanics
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What is the difference between speed and velocity?
What is the difference between speed and velocity?
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Velocity includes direction; speed does not. Velocity is a vector; speed is a scalar quantity.
Velocity includes direction; speed does not. Velocity is a vector; speed is a scalar quantity.
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How is acceleration related to velocity?
How is acceleration related to velocity?
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Acceleration is the rate of change of velocity. Describes how quickly velocity changes over time.
Acceleration is the rate of change of velocity. Describes how quickly velocity changes over time.
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Calculate the time for displacement $\Delta x = 50 \text{ m}$ with $v = 10 \text{ m/s}$.
Calculate the time for displacement $\Delta x = 50 \text{ m}$ with $v = 10 \text{ m/s}$.
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$t = 5 \text{ s}$. Using $t = \frac{\Delta x}{v}$ for constant velocity.
$t = 5 \text{ s}$. Using $t = \frac{\Delta x}{v}$ for constant velocity.
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What is the area under a velocity-time graph?
What is the area under a velocity-time graph?
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The area represents displacement. Velocity times time gives change in position.
The area represents displacement. Velocity times time gives change in position.
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Find velocity when displacement is $20 \text{ m}$ and time is $4 \text{ s}$.
Find velocity when displacement is $20 \text{ m}$ and time is $4 \text{ s}$.
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$v = 5 \text{ m/s}$. Using $v = \frac{\Delta x}{\Delta t}$ formula.
$v = 5 \text{ m/s}$. Using $v = \frac{\Delta x}{\Delta t}$ formula.
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What is the definition of uniform acceleration?
What is the definition of uniform acceleration?
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Acceleration that does not change over time. Constant rate of velocity change over time.
Acceleration that does not change over time. Constant rate of velocity change over time.
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What is the initial velocity if $v = 20 \text{ m/s}$, $a = 2 \text{ m/s}^2$, $t = 5 \text{ s}$?
What is the initial velocity if $v = 20 \text{ m/s}$, $a = 2 \text{ m/s}^2$, $t = 5 \text{ s}$?
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$v_i = 10 \text{ m/s}$. Using $v = v_i + at$ and solving for $v_i$.
$v_i = 10 \text{ m/s}$. Using $v = v_i + at$ and solving for $v_i$.
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What does a flat line on a velocity-time graph indicate?
What does a flat line on a velocity-time graph indicate?
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Constant velocity. Zero slope means no change in velocity over time.
Constant velocity. Zero slope means no change in velocity over time.
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Calculate the acceleration given $\Delta v = 15 \text{ m/s}$ and $\Delta t = 3 \text{ s}$.
Calculate the acceleration given $\Delta v = 15 \text{ m/s}$ and $\Delta t = 3 \text{ s}$.
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$a = 5 \text{ m/s}^2$. Using $a = \frac{\Delta v}{\Delta t}$ formula directly.
$a = 5 \text{ m/s}^2$. Using $a = \frac{\Delta v}{\Delta t}$ formula directly.
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Find final velocity if $v_i = 5 \text{ m/s}$, $a = 3 \text{ m/s}^2$, $t = 4 \text{ s}$.
Find final velocity if $v_i = 5 \text{ m/s}$, $a = 3 \text{ m/s}^2$, $t = 4 \text{ s}$.
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$v_f = 17 \text{ m/s}$. Using $v_f = v_i + at$ kinematic equation.
$v_f = 17 \text{ m/s}$. Using $v_f = v_i + at$ kinematic equation.
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What is the effect of doubling time on displacement in uniform acceleration?
What is the effect of doubling time on displacement in uniform acceleration?
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Displacement quadruples. Since $\Delta x \propto t^2$ for constant acceleration.
Displacement quadruples. Since $\Delta x \propto t^2$ for constant acceleration.
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Calculate the displacement given $v = 5 \text{ m/s}$ and $t = 10 \text{ s}$.
Calculate the displacement given $v = 5 \text{ m/s}$ and $t = 10 \text{ s}$.
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$\Delta x = 50 \text{ m}$. Using $\Delta x = vt$ with constant velocity.
$\Delta x = 50 \text{ m}$. Using $\Delta x = vt$ with constant velocity.
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What is the area under a velocity-time graph?
What is the area under a velocity-time graph?
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The area represents displacement. Velocity times time gives change in position.
The area represents displacement. Velocity times time gives change in position.
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Calculate displacement for $v_i = 3 \text{ m/s}$, $a = 2 \text{ m/s}^2$, $t = 4 \text{ s}$.
Calculate displacement for $v_i = 3 \text{ m/s}$, $a = 2 \text{ m/s}^2$, $t = 4 \text{ s}$.
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$\Delta x = 28 \text{ m}$. Using $\Delta x = v_i t + \frac{1}{2}at^2$ formula.
$\Delta x = 28 \text{ m}$. Using $\Delta x = v_i t + \frac{1}{2}at^2$ formula.
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Find velocity when displacement is $20 \text{ m}$ and time is $4 \text{ s}$.
Find velocity when displacement is $20 \text{ m}$ and time is $4 \text{ s}$.
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$v = 5 \text{ m/s}$. Using $v = \frac{\Delta x}{\Delta t}$ formula.
$v = 5 \text{ m/s}$. Using $v = \frac{\Delta x}{\Delta t}$ formula.
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Calculate acceleration for $v_i = 0 \text{ m/s}$, $v_f = 10 \text{ m/s}$, and $t = 5 \text{ s}$.
Calculate acceleration for $v_i = 0 \text{ m/s}$, $v_f = 10 \text{ m/s}$, and $t = 5 \text{ s}$.
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$a = 2 \text{ m/s}^2$. Using $a = \frac{\Delta v}{\Delta t} = \frac{10-0}{5}$.
$a = 2 \text{ m/s}^2$. Using $a = \frac{\Delta v}{\Delta t} = \frac{10-0}{5}$.
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State the formula for displacement in uniformly accelerated motion.
State the formula for displacement in uniformly accelerated motion.
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$\Delta x = v_i t + \frac{1}{2} a t^2$. Kinematic equation for position with constant acceleration.
$\Delta x = v_i t + \frac{1}{2} a t^2$. Kinematic equation for position with constant acceleration.
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What is the definition of uniform acceleration?
What is the definition of uniform acceleration?
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Acceleration that does not change over time. Constant rate of velocity change over time.
Acceleration that does not change over time. Constant rate of velocity change over time.
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What is the initial velocity if $v = 20 \text{ m/s}$, $a = 2 \text{ m/s}^2$, $t = 5 \text{ s}$?
What is the initial velocity if $v = 20 \text{ m/s}$, $a = 2 \text{ m/s}^2$, $t = 5 \text{ s}$?
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$v_i = 10 \text{ m/s}$. Using $v = v_i + at$ and solving for $v_i$.
$v_i = 10 \text{ m/s}$. Using $v = v_i + at$ and solving for $v_i$.
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What does it mean if displacement is negative?
What does it mean if displacement is negative?
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The final position is less than the initial position. Object moved backward from its starting position.
The final position is less than the initial position. Object moved backward from its starting position.
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What does a flat line on a velocity-time graph indicate?
What does a flat line on a velocity-time graph indicate?
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Constant velocity. Zero slope means no change in velocity over time.
Constant velocity. Zero slope means no change in velocity over time.
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Calculate the acceleration given $\Delta v = 15 \text{ m/s}$ and $\Delta t = 3 \text{ s}$.
Calculate the acceleration given $\Delta v = 15 \text{ m/s}$ and $\Delta t = 3 \text{ s}$.
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$a = 5 \text{ m/s}^2$. Using $a = \frac{\Delta v}{\Delta t}$ formula directly.
$a = 5 \text{ m/s}^2$. Using $a = \frac{\Delta v}{\Delta t}$ formula directly.
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What does the area under an acceleration-time graph represent?
What does the area under an acceleration-time graph represent?
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Change in velocity. Acceleration times time gives velocity change.
Change in velocity. Acceleration times time gives velocity change.
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Find final velocity if $v_i = 5 \text{ m/s}$, $a = 3 \text{ m/s}^2$, $t = 4 \text{ s}$.
Find final velocity if $v_i = 5 \text{ m/s}$, $a = 3 \text{ m/s}^2$, $t = 4 \text{ s}$.
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$v_f = 17 \text{ m/s}$. Using $v_f = v_i + at$ kinematic equation.
$v_f = 17 \text{ m/s}$. Using $v_f = v_i + at$ kinematic equation.
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Define average velocity.
Define average velocity.
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Average velocity is the total displacement divided by total time. Total displacement over total time elapsed.
Average velocity is the total displacement divided by total time. Total displacement over total time elapsed.
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Calculate the time for displacement $\Delta x = 50 \text{ m}$ with $v = 10 \text{ m/s}$.
Calculate the time for displacement $\Delta x = 50 \text{ m}$ with $v = 10 \text{ m/s}$.
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$t = 5 \text{ s}$. Using $t = \frac{\Delta x}{v}$ for constant velocity.
$t = 5 \text{ s}$. Using $t = \frac{\Delta x}{v}$ for constant velocity.
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What is the formula for average velocity in terms of initial and final velocity?
What is the formula for average velocity in terms of initial and final velocity?
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$v_{avg} = \frac{v_i + v_f}{2}$. Valid only for constant acceleration motion.
$v_{avg} = \frac{v_i + v_f}{2}$. Valid only for constant acceleration motion.
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What is the effect on velocity when acceleration is zero?
What is the effect on velocity when acceleration is zero?
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Velocity remains constant. No acceleration means no velocity change occurs.
Velocity remains constant. No acceleration means no velocity change occurs.
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Find final velocity if $v_i = 0$, $a = 9.8 \text{ m/s}^2$, $\Delta x = 19.6 \text{ m}$.
Find final velocity if $v_i = 0$, $a = 9.8 \text{ m/s}^2$, $\Delta x = 19.6 \text{ m}$.
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$v_f = 19.6 \text{ m/s}$. Using $v_f^2 = v_i^2 + 2a\Delta x$ equation.
$v_f = 19.6 \text{ m/s}$. Using $v_f^2 = v_i^2 + 2a\Delta x$ equation.
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What is the formula for displacement from initial and final velocity and time?
What is the formula for displacement from initial and final velocity and time?
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$\Delta x = \frac{(v_i + v_f)}{2} \cdot t$. Average velocity times time equals displacement.
$\Delta x = \frac{(v_i + v_f)}{2} \cdot t$. Average velocity times time equals displacement.
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