# High School Physics : Kinematic Equations

## Example Questions

### Example Question #142 : Linear Motion

Trevor is traveling  when he sees a red light ahead.  His car is capable of decelerating at a rate of .  If it takes him  to get the brakes on and he is  from the intersection when he sees the light, how far from the beginning of the intersection will he be, and in what direction? In other words, will he be able to stop in time?

No, he will not be able to stop in time and will stop about  beyond the intersection.

Yes, he will be able to stop in time and will stop about  before the intersection.

No, he will not be able to stop in time and will stop about  beyond the intersection.

Yes, he will be able to stop in time and will stop about  before the intersection.

No, he will not be able to stop in time and will stop about  beyond the intersection.

Explanation:

Knowns:

Unknowns:

that Trevor actually travels = ?

Equation:

Since Trevor takes a moment to react before stepping on the breaks, determine how far Trevor travels during the reaction time. At this time he is traveling at a constant velocity.

Next, using kinematic equations to determine where Trevor stops his car based on the acceleration of his car.

beyond the reaction point

Total distance traveled is the reaction time distance plus the distance traveled during the deceleration period.

total distance traveled

To find the distance beyond the red light, subtract the distance traveled from the distance to the light

distance beyond red light

### Example Question #143 : Linear Motion

Along a highway there is an unmarked police car traveling a constant .  The officer is passed by a speeder traveling .  Precisely  after the speeder passes, the officer steps on the accelerator to catch the speeder.  If the police car’s acceleration is , how much time passes before the police car overtakes the speeder? Assume here that the speeder is moving at a constant speed.

Not enough information is provided

Explanation:

Knowns:

Unknowns:

Equation:

To make things easier, set the frame of reference to the police officer.  This means that the police officer is traveling at 0km/h and the speeder is moving at a speed relative to the officer.

So the new relative velocities are:

This will help make the math easier.

Convert the relative velocity of the speeder to m/s.

Now there are two equations that have to be true for the officer to catch up to the speeder.

There are two things that connect these equations.  First, the distance that the officer travels and the speeder travels must be the same.  Additionally the final velocity of both the officer and the speeder must be the same.

Rearrange the speeder equation for the distance traveled.

Set the two equations equal, as the distance traveled of the speeder is equal to the distance traveled by the officer.

Remember that the reference point is at the officer’s perspective so the officer has an initial velocity of 0m/s.

Rewrite the equation breaking up the change of time into time final and time initial.

Distribute on the left side.

Substitute values

Simplify

Remember that the final time for both the officer and the speeder are the same.  So rearrange this in the form of a quadratic equation.

Use the quadratic formula to solve.

Since the officer did not move until , then the second answer must be correct.

### Example Question #141 : Linear Motion

Usain Bolt accelerates from rest to  over a distance of . What is his acceleration? Assume the acceleration is constant.

Explanation:

We are given final velocity and we know initial velocity is 0. We can use the following kinematics formula to relate final speed, initial speed, acceleration, and displacement:

The initial velocity is zero since Usain starts from rest. Therefore we can remove it from the equation.

Rearrange the equation to solve for acceleration.

### Example Question #142 : Linear Motion

Peter starts from rest and runs down a hallway . If his final velocity is , how far did he run?

Explanation:

Knowns:

Unknowns:

Equation:

First we need to determine Peter’s acceleration. The best kinematic equation to use here is:

Once Peter’s acceleration is known it is possible to find the distance he traveled.

Peter’s initial velocity is  so this equation simplifies to

### Example Question #146 : Linear Motion

Objects  and  both start from rest.  They both accelerate at the same rate.  However, object  accelerates for twice the time as object .  What is the distance traveled by object  compare to that of object ?

The same distance

Four times as far

Three times as far

Twice as far

Four times as far

Explanation:

The distance traveled is directly related to the square of the time traveled.  Therefore time if time is doubled, the value will be squared and therefore four times as great.  The distance traveled will be 4 times as far.

### Example Question #1 : Kinematic Equations

Suppose a can is kicked and then travels up a smooth hill of ice.  Which of the following is true about its acceleration?

It will travel at constant velocity with zero acceleration

It will have the same acceleration, both up the hill and down the hill.

It will have a constant acceleration up the hill, but a different constant acceleration when it comes back down

It will have a varying acceleration along the hill.

It will have the same acceleration, both up the hill and down the hill.

Explanation:

The can will have the same acceleration both up and down the hill since there is no friction.  Friction or other forces would cause a change in acceleration.  But since there is no friction, the can will travel up the hill, slow down and then accelerate back down the hill.

### Example Question #148 : Linear Motion

A runner wants to complete a  run in less than .  After running at constant speed for exactly , the runner still has  left to run.  The runner must then accelerate at  for how many seconds in order to reach a final velocity that will allow them to complete the  left of the race in the desired time?

Explanation:

Knowns:

Unknown:

Equation:

The first thing is to determine the initial velocity of the runner before the runner accelerates for the final portion of the race.  Since the runner is traveling at a constant velocity

Next, convert the time during the constant speed portion to seconds.

Determine the amount of distance traveled while at a constant speed.

Use these values to determine the velocity of the runner.

Next determine the final velocity needed for the runner to finish out the race in the remaining time.

left in race

Finally use the kinematic equations to calculate the time needed to get to this velocity.

Rearrange for time

### Example Question #149 : Linear Motion

A ball rolls to a stop after . If it had a starting velocity of , what is the deceleration on the ball due to friction?

Explanation:

Explanation:

We are given the initial velocity, time, and final velocity (zero because the ball stops). Using these values and the appropriate motion equation, we can solve for the acceleration.

Acceleration is given by the change in velocity over time:

We can use our values to solve for the acceleration.

### Example Question #150 : Linear Motion

Objects  and  both start at rest.  They both accelerate at the same rate.  However, object  accelerates for twice the time as object . What is the final speed of object  compared to that of object

Four times as fast

The same speed

Twice as fast

Three times as fast