1D Kinematics Archives • Nerd Notes

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A car moves forward at a steady \( 10 \) \( \text{m/s} \) for \( 5 \) \( \text{s} \). The driver slams the brakes and brings it to rest in \( 2 \) \( \text{s} \). Without waiting, the driver immediately accelerates backward (negative velocity) for \( 3 \) \( \text{s} \) until reaching \( 8 \) \( \text{m/s} \) in reverse. Draw the velocity vs. time graph.

An elevator starts at rest on the ground floor. It accelerates upward smoothly for \( 2 \) \( \text{s} \) until reaching a steady upward speed. It continues at that constant speed for \( 5 \) \( \text{s} \) before gently slowing to rest at the next floor in \( 3 \) \( \text{s} \). Draw the velocity vs. time graph.

A skater glides across the ice at a constant \( 6 \) \( \text{m/s} \). After \( 4 \) \( \text{s} \), friction gradually slows them down until they come to rest in \( 6 \) \( \text{s} \). They pause for \( 2 \) \( \text{s} \), then push off in the opposite direction, steadily gaining speed for \( 5 \) \( \text{s} \). Draw the velocity vs. time graph.

A rollercoaster leaves the station at rest. Its speed increases steadily for \( 6 \) \( \text{s} \) as it heads down the first drop. The ride then levels out and it moves at a constant speed for \( 4 \) \( \text{s} \) before hitting the brakes and stopping in \( 3 \) \( \text{s} \). Draw the velocity vs. time graph.

You throw a ball straight upward. It leaves your hand at \( 20 \) \( \text{m/s} \) and slows at a steady rate until it stops at the peak. The ball then comes back down, speeding up steadily until it hits the ground with the same speed it left your hand. Draw the velocity vs. time graph.

Given the graph of velocity versus time for a duck flying due south for the winter, at what labeled point did the duck stop its forward motion?

A projectile is launched at \( 25 \) \( \text{m/s} \) at an angle of \( 37^{\circ} \). It lands on a platform that is \( 5.0 \) \( \text{m} \) above the launch height.

Person A throws a ball horizontally from a cliff \( 20 \) \( \text{m} \) tall at \( 12 \) \( \text{m/s} \). Person B is running to the right on the ground and catches the ball at the same height it would’ve landed after running \( 15 \) \( \text{m} \).Find: How fast was Person B running?

A projectile is launched at \( 25 \) \( \text{m/s} \) at an angle of \( 45^\circ \). It lands on a slope \( 5 \) \( \text{m} \) below the launch height. On landing, it rebounds vertically with \( 80\% \) of its speed and falls straight down from there. Find the total time from launch to final impact at the base of the slope.

A projectile is launched at a speed of \( 22 \) \( \text{m/s} \) at an angle of \( 60^{\circ} \) above the horizontal. It lands on a ramp that is \( 5 \) \( \text{m} \) lower than the launch height. How long does it take for the projectile to hit the ramp?

A ball is launched horizontally from a height. At the same time, another ball is dropped vertically from the same height. Which hits the ground first?

A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge that is \( 235 \) \( \text{m} \) below. The plane is traveling horizontally with a speed of \( 250 \) \( \text{km/h} \). How far in advance of the recipients (horizontal distance) must the goods be dropped?

A projectile has the least speed at what point in its path?

Ball A is dropped from the top of a cliff. At the same time, Ball B is thrown straight upward from the ground at \( 30 \) \( \text{m/s} \). The two balls pass each other after \( 2.0 \) \( \text{s} \).

A car is driving to the right at \( 20 \) \( \text{m/s} \). A motorcycle starts \( 30 \) \( \text{m} \) behind the car and is moving at \( 30 \) \( \text{m/s} \) in the same direction.

Runner A begins a \( 100 \)-meter race at time \( t = 0 \) and runs at a constant speed of \( 6.0 \) \( \text{m/s} \). Runner B starts the same race \( 3 \) seconds later but runs at \( 9.0 \) \( \text{m/s} \).

Two students start \( 100 \) \( \text{m} \) apart.• Student A walks to the right at \( 2 \) \( \text{m/s} \).• Student B walks to the left at \( 3 \) \( \text{m/s} \).At what time do the students meet, and how far has each student walked when they collide?

A baseball is seen to pass upward by a window with a vertical speed of \( 14 \) \( \text{m/s} \). If the ball was thrown by a person \( 18 \) \( \text{m} \) below on the street, determine the following.

A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard \( 3.4 \) \( \text{s} \) later. If the speed of sound is \( 340 \) \( \text{m/s} \), how high is the cliff?

A driver is traveling at a speed of \( 18.0 \) \( \text{m/s} \) when she sees a red light ahead. Her car is capable of decelerating at a rate of \( 3.65 \) \( \text{m/s}^2 \). If it takes her \( 0.350 \) \( \text{s} \) to get the brakes on and she is \( 20.0 \) \( \text{m} \) from the intersection when she sees the light, will she be able to stop in time? How far from the beginning of the intersection will she be, and in what direction?

Mary and Sally are in a foot race. When Mary is \( 22 \) \( \text{m} \) from the finish line, she has a speed of \( 4.0 \) \( \text{m/s} \) and is \( 5.0 \) \( \text{m} \) behind Sally, who has a speed of \( 5.0 \) \( \text{m/s} \). Sally thinks she has an easy win and, during the remaining portion of the race, decelerates at a constant rate of \( 0.40 \) \( \text{m/s}^2 \) until she reaches the finish line. What constant acceleration must Mary maintain during the remaining portion of the race if she wishes to cross the finish line side-by-side with Sally?

A ball is thrown straight up. What are the velocity and acceleration of the ball at the highest point in its path?

Can an object have \( 0 \) velocity and nonzero acceleration at the same time? Give examples.

A stone is thrown vertically upwards with a speed of \( 20.0 \) \( \text{m/s} \). How fast is it moving when it reaches a height of \( 12.0 \) \( \text{m} \)?

You are a bungee jumping fanatic and want to be the first bungee jumper on Jupiter. The length of your bungee cord is \( 45.0 \) \( \text{m} \). Free fall acceleration on Jupiter is \( 23.1 \) \( \text{m/s}^2 \). What is the ratio of your speed on Jupiter to your speed on Earth when you have dropped \( 45 \) \( \text{m} \)? Ignore the effects of air resistance and assume that you start at rest.

A ball is thrown straight up with a speed of \( 30 \) \( \text{m/s} \), and air resistance is negligible.

A car slows down uniformly from a speed of \( 28.0 \) \( \text{m/s} \) to rest in \( 8.00 \) \( \text{s} \). How far did it travel in that time?

A helicopter is ascending vertically with a speed of \( 5.40 \) \( \text{m/s} \). At a height of \( 105 \) \( \text{m} \) above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground?

A kangaroo jumps straight up to a vertical height of \( 1.45 \) \( \text{m} \). How long was it in the air before returning to Earth?

A stone is thrown vertically upward with a speed of \( 24.0 \) \( \text{m/s} \).

Can an object have a non-zero distance and zero average speed?

A student walks \( 3 \) \( \text{m} \) east, then \( 4 \) \( \text{m} \) west in \( 7 \) \( \text{s} \). What is their displacement and average velocity?

Which pair of quantities will always have the same magnitude if motion is in a straight line and in one direction?

A car travels \( 60 \) \( \text{km} \) at \( 30 \) \( \text{km/h} \), then \( 60 \) \( \text{km} \) at \( 60 \) \( \text{km/h} \). What is its average speed over the entire trip?

Which of the following can never be negative?

A runner completes one full lap around a \( 400 \) \( \text{m} \) track in \( 100 \) \( \text{s} \). What is their average velocity?

An object is moving in the \( +x \) direction and begins to slow down. What must be true about its acceleration?

A ball rolls down a ramp and gains speed. Its velocity is increasing in the negative direction. What can be said about its acceleration?

Which car controls directly allow the driver to cause acceleration?

A car is heading rightward but accelerating to the left. This means the car is:

Which of these scenarios involve accelerated motion? (Select all that apply)

If something is accelerating, then it must be… (Select all that apply)

A car travels east at a steady \( 30 \) \( \text{m/s} \) for \( 5 \) \( \text{s} \). What is its acceleration during this motion?

An object can move upward while having a downward acceleration.

When we refer to an object’s speed, we’re talking about:

A teacher walks the following path in \( 10 \) \( \text{s} \): \( 2 \) \( \text{m} \) south, \( 4 \) \( \text{m} \) east, \( 2 \) \( \text{m} \) north, \( 4 \) \( \text{m} \) west. What is the teacher’s average velocity?

What does displacement mean in the context of motion?

What does distance represent during any type of motion?

A car’s velocity increases as follows each second: \( 2 \) \( \text{m/s} \), \( 4 \) \( \text{m/s} \), \( 6 \) \( \text{m/s} \), \( 8 \) \( \text{m/s} \). This pattern shows that the car is:

How is acceleration defined?