Knowns:

Unknowns:

Time can be broken up as well.  There is a time that it takes the ball to roll down the lane to hit the pin.  There is also a different time for the sound to reach the person’s ear.  This adds up to the total time provided in the problem.

Equation:

The ball and sound both travel at constant velocities.  Therefore the equation that can best be used is

Each step must be taken into account as the ball travels down the alley and as the sound travels back.  Since the velocity of the ball is not provided, the best place to start is to find the amount of time that it takes for the sound to reach the person’s ear.

Rearrange the equation to solve for time.

Plug in the values for the speed of sound and the distance that the sound travels.

The total time was given.  Subtract the time that it takes the sound to travel to determine how long the ball was rolling down the lane.

Now, use this time in the equation with the distance of the bowling to determine the velocity of the ball

Knowns:

Unknowns:

Equation: 

To solve this problem we need to consider the definition of speed, which is the distance traveled over a given amount of time.

Even though the player's speed is changing throughout the sprint (due to acceleration), we are asked to find the average speed. We can do this using the total distance and total time given. The distance is  and the time is .

Assuming you stand in one place, the distance between you and the lightning strike does not change. 

The formula for velocity is:

In this scenario, the distance travelled, , does not change. The time taken to travel this distance,  , does change. That means that the velocity must also be changing.

This is an indirect relationship. As  increases,  will decrease; thus, the object with a greater time of travel (sound) will have a slower velocity.

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.

If the velocity doubles every second, and it starts with a velocity of , then after  it would have a velocity of:

After  it would have a velocity of:

After  it would have a velocity of:

The basic formula for final velocity is:

Since the ball starts at rest, we can simplify the equation by removing the initial velocity.

Since the acceleration on the ball will be the acceleration due to gravity, , and the time will be , as per the problem, we can insert these variables into the equation to get our answer.

Acceleration is the change in velocity over the change in time.

We are given the initial and final velocities, as well as the change in time. We can use these values to calculate the acceleration.

For this question, we will need to use the acceleration formula:

We are given the initial velocity, final velocity, and time. Using these values in the equation, we can solve for the acceleration.

Note that the acceleration is negative, showing that the ball is slowing down, or decelerating.

To solve this problem use the equation:

We are given the acceleration and time, and we can assume the initial velocity is zero since the car starts from rest. Use these values to solve for the final velocity.

Acceleration is equal to a change in velocity divided by a change in time.

.

Since the car starts at rest, the initial velocity is zero. We know the acceleration and the change in time. Using these values, we can solve for the final velocity.

We can plug in our given values and solve: