Peoples Physics Book Version-2

4.5. One Dimensional Examples http://www.ck12.org

vf^2 =vi^2 + 2 ax⇒

vf^2 −vi^2

2 a

=x

We can now substitute in the known values to get x.

vf^2 −vi^2

2 a

=

(0m/s− 702 m/s)

2 ×(− 9 .8m/s^2 )

=250m

b) To solve for the total time the ball is in the air we will for the time that the ball is traveling up and double it (the
trip down will take the same time as the trip up). We know the initial velocity is 70m/s and the acceleration due to
gravity is− 9 .8m/s^2. We also know that the final velocity is 0m/s. We will use the equationvf=vi+atand solve
for t.

vf=vi+at⇒

vf−vi

a

=t

We can now substitute what we know into the equation to solve for t.

vf−vi

a

=

0m/s−70m/s

− 9 .8m/s^2

=7sec

Remember that this is only the trip up though. To solve for the total time the ball in the air we simply double the
answer.

7sec× 2 =14sec

c) We know the ceiling height(237m), the initial velocity (70m/s), and the acceleration (− 9 .8m/s^2 ). Using the
equationvf^2 =vi^2 + 2 ax, we can solve for v.

vf^2 =vi^2 + 2 ax⇒vf=

√

vi^2 + 2 ax

We can now find the velocity.

√

vi^2 + 2 ax=

√

702 m/s+ 2 ×(− 9 .8m/s^2 )×(237m) =16m/s

Example 3

Question: Two cars are heading toward each other, traveling at 50km/hr (car A) and 70km/hr (car B). They are 12km
apart. How much time do they have before they collide?

Answer: To find the answer, we must find the proportion of the distance that each car travels. In the time that car A
travels 50km, car B will travel 70km. This can be made into the ratio^5070 which can then be simplified into^57. This