# High School Physics : Understanding Motion in One Dimension

## Example Questions

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### Example Question #1 : Linear Motion

Laura throws a ball vertically. She notices it reaches a maximum height of 10 meters. What was the initial velocity of the ball?

Possible Answers:

Correct answer:

Explanation:

Remember that at the highest point, the velocity in the y-direction is equal to zero. Using the given values and the equation below, we can solve for the initial velocity.

### Example Question #2 : Understanding Motion In One Dimension

Marcus throws a ball directly up in the air with an initial velocity of . How high will the ball go?

Possible Answers:

Correct answer:

Explanation:

Remember that the final velocity at an object's highest point is equal to zero. We can use the following equation to solve for our height (), using the initial velocity, final velocity, and acceleration due to gravity.

### Example Question #1 : Understanding Motion In One Dimension

A picture hanging  above the ground falls off the wall and hits the ground. What is its final velocity?

Possible Answers:

Correct answer:

Explanation:

The problem gives us the distance, the acceleration due to gravity, and implies that the initial velocity of the picture is zero, as it starts at rest.

We can find the final velocity using the appropriate motion equation:

We can use our values to solve for the final velocity. Keep in mind that the displacement will be negative because the ball is traveling in the downward direction!

The square root of a term can be either positive or negative, depending on the direction. Since velocity is a vector, and the painting is falling downward, our final answer will be negative: .

### Example Question #4 : Understanding Motion In One Dimension

An object moves at a constant velocity, , for some distance, . How long it in motion?

Possible Answers:

Correct answer:

Explanation:

The relationship between velocity, distance, and time is:

We can multiply both sides by the time, then divide both sides by the velocity, to isolate the variable for time.

The quotient of distance and velocity will give us the time that the object was in motion.

### Example Question #5 : Understanding Motion In One Dimension

A ball is thrown vertically with a velocity of . What is its velocity at the highest point in the throw?

Possible Answers:

There is insufficient information to solve

Correct answer:

Explanation:

When examining vertical motion, the vertical velocity will always be zero at the highest point. At this point, the acceleration from gravity is working to change the motion of the ball from positive (upward) to negative (downward). This change is represented by the x-axis on a velocity versus time graph. As the ball changes direction, its velocity crosses the x-axis, momentarily becoming zero.

### Example Question #6 : Understanding Motion In One Dimension

Part of competing in a triathlon involves swimming in the open water. Suppose a woman competing swims at a speed of  in still water and needs to swim . On the day of this particular race, there is an opposing current of  going directly against the swimmer. How long does it take for her to finish the swim?

Possible Answers:

Correct answer:

Explanation:

The woman needs to swim , or . She normally swims at , but has a current opposing her. The effect will make her relative velocity equal to her normal velocity, minus the current against her.

We know that velocity is a change in distance divided by a change in time. Now that we have her relative velocity and the distance traveled, we can isolate the time variable and solve for her time.

### Example Question #7 : Understanding Motion In One Dimension

Suppose a recreational biker averages  on a twenty-mile ride, equal to . A professional biker has an average speed of . The professional happens to be riding on the same path, but started  behind the recreational biker. The two are both headed for the same destination. Who would reach the end of the path first, and how far behind would the other biker be?

Possible Answers:

The professional finishes first and the other biker is  behind

The recreational finishes first and the other biker is  behind

The recreational finishes first and the other biker is  behind

Both bikers reach destination at same time

The professional finishes first and the other biker is  behind

Correct answer:

The professional finishes first and the other biker is  behind

Explanation:

To solve this problem we can simply examine each biker separately and see how long it would take them to reach the destination. Let's begin with the recreational biker. The recreational biker needs to ride  at . Using the definition of velocity, we can find his final time.

The professional has a distance of , plus the  that he's behind.

We know that the velocity of the professional biker is . Using this velocity and his total distance, we can find the time that it takes him to reach the end of the path.

The time of the professional biker is less than that of the recreational biker, meaning that the professional will finish first. Now we need to find the distance between the two bikers at this point. Use the recreational biker's velocity and the time difference between the two bikers to solve for the distance that the recreational biker has left on the path.

The recreational biker will ride for at to finish the path.

### Example Question #8 : Understanding Motion In One Dimension

A picture hanging  above the ground falls off the wall and hits the ground. How long will it be before it hits the ground?

Possible Answers:

Correct answer:

Explanation:

The problem gives us the distance, the acceleration due to gravity, and implies that the initial velocity of the picture is zero, as it starts at rest.

We can use the appropriate motion equation to solve for the final velocity:

We can use our values to solve for the time. Keep in mind that the displacement will be negative because the ball is traveling in the downward direction!

### Example Question #9 : Understanding Motion In One Dimension

Jenny throws a ball directly up in the air. She notices that it changes direction after approximately 3 seconds. What was the initial velocity of the ball?

Possible Answers:

Correct answer:

Explanation:

The ball will travel upwards to the highest point, then change direction and travel downwards. Remember that the velocity in at the highest point is equal to zero. We can use the following equation and our known data to solve for the initial velocity.

### Example Question #10 : Understanding Motion In One Dimension

A ball rolls along a table with a constant velocity of . If it rolls for , how long was it rolling?

Possible Answers:

Correct answer:

Explanation:

The relationship between constant velocity, distance, and time can best be illustrated as .

We are given the velocity and the distance, allowing us to solve for the time that the ball was in motion.

Isolate the variable for time.

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