# Sample Kinematics Problems with Solutions

Reference > Science > Physics > Study Guide > Unit 1: Kinematics - Motion in One Direction_{avg}=

_{avg}=

_{avg}=

_{i}+ v

_{f}

_{f}= v

_{i}+ aΔt

_{i}Δt +

^{2}

_{f}

^{2}= v

_{i}

^{2}+ 2aΔd

##

Sample Problem #1

A car starts from rest and accelerates with a uniform acceleration of 10 ^{2}

## Sample Solution #1

_{i}

^{2}

_{f}

This problem can be solved by a straight forward application of equation 4 to find Δt and equation 5 to find ΔX. The student should demonstrate that the correct answers are Δt=9 s and ΔX=405 ft. It is a good idea to try to find the answers using slightly different procedures whenever possible. For example, in this problem a quick check can be made by using your calculated value for Δt, from equation 4 to find the average speed and then set X=V_{avg}Δt to get 405 ft a different way. A second different method would be to use equation 6 and the value of Δt obtained from equation 4 to calculate ΔX. However, while both of the alternate techniques are good checks on the validity of your calculations it is best to avoid using an answer to one part as a basis for a second calculation whenever possible.

## Sample Problem #2

A car moving at 30## Sample Solution #2

_{i}

_{f}

^{2}

## Sample Problem #3

Explain the significance of the negative sign in problem 2.

## Sample Solution #3

The acceleration is in the negative direction. Since V was arbitrarily assigned a positive direction, the acceleration must be in the opposite direction.

## Sample Problem #4

Assume that the car in problem 2 keeps the same acceleration for an additional 5 seconds. Find its speed and position at the end of this time.

## Sample Solution #4

_{i}

^{2}

_{f}

^{2}

## Sample Problem #5

A baseball is batted vertically with an initial speed of 45(a) the time before it returns to the level at which it started.

(b) the maximum height the ball reaches.

(c) the position, speed and acceleration 6 seconds after it is batted.

(d) the position and speed 12 seconds after it is batted.

## Sample Solution #5

Read this problem carefully and decide the order that you will do the problem. Keep in mind the facts mentioned in the hints such as: the time to reach the top is equal to one-half the total time in the air; the speed at the top is zero; and the speed when it reaches the same level is the same as the initial speed. In multi part problems such as this one, it will be necessary to list the given quantities for each part. As you solve the problem, check to be sure the answers to the various sections are consistent with each other. Before starting the problem decide which direction to call positive. In this problem we will call the upward direction positive and the downward direction negative.

(a)_{i}

_{f}

^{2}

_{i}

_{f}

^{2}

_{i}

^{2}

_{f}

^{2}

## Sample Problem #6

A ball dropped from the roof of a tall building passed a window ledge with a speed of 96(a) What is the height of the window?

(b) How tall is the building?

## Sample Solution #6

(a)
_{i}

^{2}

_{i}. ΔX can be easily found by applying equation 6.(ans: ΔX = 112 ft) Since this is the distance the ball fell during the last second, it must be the height of the window.

_{i}

_{f}

^{2}

## Questions

^{2}for 3.0sec. What is its final speed? How far does it travel? What is the average speed during the 3.0sec?

^{2}) sustained by the safety belt the driver was, of course, wearing. How many times greater would the acceleration be if the initial velocity were 60 mph?