Peoples Physics Book Version-2

http://www.ck12.org Chapter 4. One Dimensional Motion Version 2

4.5 One Dimensional Examples

Example 1

Question: If Bob walks 100 meters north, turns around, and walks 100 meters south, what is his total distancedand
displacement∆~x?

Solution: If Bob walked 100 meters in north, turned around, and walked back to his starting position his total
distance traveled would be:

d=|∆~x 1 |+|∆~x 2 |=|100m|+|−100m|=200m.

However, his displacement would be:

f - _i = 0 m + 0 m = 0 m.∆~x=~x

As you can see, if Bob returns to his original starting position his displacement (0 meters) and his total distance
traveled (200 meters) are very different.

Example 2

Question: Joe throws a ball straight up with a initial velocity of 70ms. For this problem ignore Joe’s height.

a) How high does the ball go?

b) For how many seconds is the ball in the air?

c) Joe is now standing underneath a ceiling that is 237m high. How fast will the ball be traveling when it strikes the
ceiling?

Solution:

a) We know the initial velocity (70m/s^2 ) and the acceleration (the only acceleration that acts upon the ball after it has
left Joe’s hand is the acceleration of gravity, which is− 9 .8m/s^2 ). We can figure out the final velocity by realizing
that when the ball is at the highest point, the velocity will be 0m/s^2. To find the height of the ball we will use the
equationvf^2 =vi^2 + 2 axand solve for x.