Extra Kinematics Equations Practice
Hints and Answers
Try the problems before you check out the hints and answers to make sure you really know
how to do the problems.
1. A ball is dropped off a cliff and takes 5.8 seconds to hit the ground. How high is the cliff?
Use the purple equation. Since it is dropped from rest, it is in free fall. You will negative displacement
because that’s how far it fell in the negative direction.
a = −9.8 m 2
vi = 0 m
1
1
s
s d = vi t + at 2 d = 0 m (5.8s ) + −9.8 m 2 (5.8s ) 2
d = 164.8m
s
s
2
2
t = 5.8s
d =?
(
)
(
)
2. A car accelerates from rest to 34 m/s in just 12 seconds. What is its acceleration?
Use the orange equation.
34 m − 0 m
vF = 34 m
vF − vi
s
s = 2.83 m
s
a=
a=
s2
12 s
t
a=?
3. A rocket shoots up 123 meters.
a. What is its initial velocity?
Use the dark green equation. If you know how high the rocket goes, and since its shot straight up
we know that its velocity at the maximum height will be zero.
d = 123m
2
a = −9.8 m 2
s vF 2 = vi 2 + 2ad 0 m
= vi 2 + 2 −9.8 m 2 (123m ) vi = 49 m
s
s
s
vF = 0 m
vi = ?
s
(
)
(
)
b. How long is it ascending? (you can use either)
Lots of options because you know now the initial velocity, any method is appropriate.and all give
the same answer.
v +v 
v −v
d = 123m
d =  F i t
a= F i
 2 
t
vF = 0 m
s
 0 m + 49 m 
0 m − 49 m
s
s t
s
s
a = −9.8 m 2
−9.8 m 2 =
123m = 
s
s
t

2



m
t = 5s
vi = 49
s
t = 5s
t =?
4. A racecar can accelerate at 8.9 m/s2; if the car starts from 10 m/s, after 2.1 seconds how fast is it going?
Use the orange equation.
t = 2.1s
a = 8.9 m 2
vF − 10 m
v −v
s
s
8.9 m 2 =
vF = ?
a= F i
vF = 28.7 m
s
s
2.1
s
t
m
vi = 10
s
5. A driver is traveling at 10.9 m/s and has a reaction time of 0.3 seconds.
a. If the driver has to slam on his brakes, how far does the car travel before he even slams on his
brakes? Similar to problems in class, this is while the driver is still moving at a constant velocity
before he begins to brake. Use the blue equation.
v = 10.9 m
s d = ? d = vt = 10.9 m (0.3s ) = 3.27 m
s
t = 0.3s
(
)
b. If the driver can decelerate at 3.8 m/s2, how far will he travel before he comes to a stop?
Now that you know the drivers acceleration, you can solve for the distance it would take him to
stop. Since he stops his final velocity is 0 m/s. Use the green equation.
vi = 10.9 m
2
2
s a = −3.8 m s 2
vF 2 = vi 2 + 2ad
0m
= 10.9 m
+ 2 −3.8 m 2 d d = 15.6m
s
s
s
m
vF = 0
d =?
s
(
) (
)
)
(
c. How far does the car travel in total before stopping?
Add the two distances together.
d1 = 3.27 m
dT = ?
dT = d1 + d 2 = 3.27 m + 15.6m = 18.87m
d 2 = 15.6m
6. If you drop something from rest off a 10.3 m high building, how long will it take to hit the ground?
Use the purple equation.
a = −9.8 m 2
vi = 0 m
1
1
s
s d = vi t + at 2 (−10.3m) = 0 m t + −9.8 m 2 t 2 t = 1.45s
s
s
2
2
d = −10.3m
t =?
(
)
)
(
7. A runner can travel 400 m in 5.2 minutes. What is their average velocity?
Since you’re looking for the average velocity you can use the blue equation.
d 400m
 60s 
d = 400m t = 5.2 min 
= 1.28 m
 = 312 s v = ? v = =
s
1min
t
312
s


8. A jet plane takes 217 meters to get to a top speed of 239 m/s from rest. What is its acceleration?
Use the green equation. Since its speeding up, you should get a positive acceleration.
d = 217 m
2
2
vi = 0 m
m
m
s vF 2 = vi 2 + 2ad
239
=
0
+ 2a(217m)
a = 131.6 m 2
s
s
s
vF = 239 m
s a=?
(
) (
)
9. How long will it take a running horse to travel 45 m and attain a speed of 7 m/s from rest?
Use the red equation.
 7m + 0m 
vF = 7 m
d = 45m
v +v 
s
s
s t
d =  F i t
45m = 
t = 12.9 s
m
2

2

t =?


vi = 0


s
10. A potato gun can launch a potato straight up with an initial velocity of 3.2 m/s. How high will the potato
go? This is a projectile shot straight up, so we know its final velocity at its maximum height will be 0
m/s. Use the green equation to solve for the height.
vF = 0 m
2
2
vi = 3.2 m
s
s
vF 2 = vi 2 + 2ad
0m
= 3.2 m
+ 2 −9.8 m 2 d d = 0.52m
s
s
s
m
a = −9.8 2 d = ?
s
(
) (
)
(
)
11. A cross country skier can travel at 4.7 m/s. If they travel for 20 minutes, how far have they gone?
Since they are traveling at a constant speed, use the blue equation.
v = 4.7 m
 60 s 
m
s
t = 20 min 
 = 1200s d = vt = 4.7 s (1200 s ) = 5640m
1min


d =?
(
)
12. A penguin slides down a hill in the Arctic in 7 seconds. If the penguin started from rest and gains a
speed of 1.9 m/s, what is its acceleration?
Use the orange equation, be sure to keep your initial and final velocities separate.
m
m
t = 7s
vF = 1.9 m
vF − vi 1.9 s − 0 s
s
a=
=
= 0.27 m 2
s
vi = 0 m
t
7
s
a=?
s
13. A bat is flying at 0.6 m/s when it spots an appetizing insect. The bat accelerates at a rate of 1.2 m/s2 for
1.9 seconds. How fast is the bat traveling at the time of that time?
Use the orange equation, be sure to keep your initial and final velocities separate.
vi = 0.6 m
vF − 0 m
vF − vi
s t = 1.9s
s v = 2.28 m
m
a=
1.2 2 =
F
s
s
m
v
=
?
t
1.9
s
F
a = 1.2 2
s
14. A dogsled can travel as fast as 6.7 m/s and can travel for hours without stopping. If the dogs travel 113
km, how long will it take them in hours?
Assume they are traveling at a constant speed and solve for the time using the blue equation. Convert
that time in seconds to hours.
v = 6.7 m
 1000m 
s
d = 113km 
d = vt
113000m = 6.7 m t
 = 113000m
s
 1km 
t =?
 1min   1hr 
t = 16865.7 s 

 = 4.7hr
 60 s   60 min 
(
)
15. A rubber bouncy ball is dropped off a balcony 19.6 meters off the ground. How long will it take it to
fall? Assume its initial velocity is zero, solve for the time it takes to fall using the purple equation.
a = −9.8 m 2
vi = 0 m
1
1
s
s d = vi t + at 2 −19.6m = 0 m t + −9.8 m 2 t 2
t = 2s
s
s
2
2
d = −19.6m
t =?
(
)
(
)
16. A speedboat accelerates from rest to 14 m/s in 0.4 seconds. What is its acceleration?
Use the orange equation, remember “from rest” means an initial velocity of 0 m/s.
m
m
vi = 0 m
t = 0.4 s
vF − vi 14 s − 0 s
s
a=
=
= 35 m 2
s
m
t
0.4
s
a
=
?
vF = 14
s
17. If you can make it from one end of a football field to the other (~100 meters) with an acceleration of 2.2
m/s2, what would your top speed be if you started from rest?
Use the green equation.
d = 100m
2
vi = 0 m
2
2
2
m
s
v
=
v
+
2
ad
v
=
0
+ 2 2.2 m 2 (100m) vF = 21 m
F
F
i
s
s
s
a = 2.2 m 2
vF = ?
s
(
)
(
)
18. a. How long would it take a penny to fall from the top of the Empire State Building if it is 381 m tall?
Use the purple equation and solve for the time.
d = −381m
vi = 0 m
1
1
s
d = vi t + at 2
−381m = 0 m t + −9.8 m 2 t 2 t = 8.81s
s
s
a = −9.8 m 2 t = ?
2
2
s
(
)
(
)
b. Assuming the penny doesn’t reach its terminal velocity, how fast, hypothetically, would it be moving
when it hit the ground?
There are several ways to solve it:
1. Use the green equation, makes sure you got it right because you don’t use the answer in part
a (time).
2. Orange equation, using the time
3. Red equation, using the time
Notice that no matter the method you get the same answer.
2
vF 2 = vi 2 + 2ad
vF 2 = 0 m
vF = (−)86.4 m
+ 2 −9.8 m 2 (−381m)
d = −381m
s
s
s
m
a = −9.8 2
vF − 0 m
vF − vi
s
s
m
a=
−9.8 2 =
vF = −86.3 m
s
s
m
t
8.81
s
vi = 0
s
 vF + 0 m 
 vF + vi 
t = 8.81s
s  (8.81s )
d =
vF = −86.5 m
−381m = 
t
s
2

2



vF = ?


(
)
)
(
19. When an airplane takes off, it gains a speed of 250 km/hr in about 244 meters. What is the planes
acceleration?
First, convert km/hr to m/s. Than use the green equation.
v F 2 = vi 2 + 2ad
vi = 0 m
s
2
2
km  1hr   1min   1000m 
m
m
m
d = 244m
vF = 250



 = 69.4 s 69.4 s = 0 s + 2a (244m)
hr  60 min   60s   1km 
a=?
a = 9.88 m 2
s
(
) (
)
20. The circumference of the Earth is roughly 40,233 km. What is the speed of the Earth’s rotation?
Convert km to m and you know that it takes the Earth 24 hours to make a full rotation. Convert hours to
seconds. Now its just a simple constant velocity problem, use the blue equation.
 1000m 
 60 min   60s 
d = 40, 233km 
t = 24hr 
 = 40, 233, 000m

 = 86400s
 1km 
 1hr   1min 
d 40, 233, 000m
v=?
v= =
= 465.7 m
s
t
86400s
Hopefully now you feel ready!