1
D Kinematics Problems
Physics Standards:
SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects.
a. Calculate average velocity, instantaneous velocity, and acceleration in a given frame of reference.
c. Compare graphically and algebraically the relationships among position, velocity, acceleration, and time
1.
A car in front of the school goes from rest to 27 m/s
in 3.0 seconds. What is its acceleration?
2.
A rocket accelerates at a rate of 190 m/s
2
for 2.4 seconds from rest. What is its final speed?
3.
A car has a velocity of 15 m/s. It then accelerates at a rate of 3.5 m/s
2
for the next 5.0 seconds. What is its final
velocity?
4.
What distance will a train stop in if its initial velocity is 23 m
/s
and its acceleration is

0.25 m/s
2
?
5.
What distance will a car cover accelerating from 12 m/s
to 26 m/s
in 14 seconds?
6.
A person starts at rest and accelerates at 3.2 m/s
2
for 3.0 seconds. What is their final velocity? What is their average
velocit
y? What distance do they cover in that time?
7.
What must be the acceleration of a train in order for it to stop from 12 m/s
in a distance of 541 m?
8.
A car will skid to a halt at a rate of

9.4 m/s
2
. If you measure skid marks that are 34 m long, with
what speed was
the car going that made them?
9.
A rock falls off a cliff and hits the ground 5
.0
seconds later. How high is the cliff?
10.
A jealous lover stands at the edge of a 50
m
tall building holding a tomato.
If a man flirting with the lover
's
girlfriend below walks at 1
m/s
towards the building, and the man is the tomato's target, at what distance should
he be from the building when the jealous lover drops the tomato?
(Assume either that the flirt has no height,
or that the tomato will hit
his spiffy new shoes.)
11.
A bat
named Lars is
flying towards a wall sends out a sound wave at a distance of 2
m
from the wall.
The sound
wave travels at 330
m/s
.
Lars
is flying at 20
m/s
, how far will
Lars
travel in the time it takes for the sound wave
to hit the wall and return to
him
?
12.
A cheetah starts from rest and runs in a straight line with a constant acceleration of 8 m/s
2
. How far does the
cheetah run between:
a)
the 1
st
and 2
nd
second (t = 1 sec to t = 2 sec)?
b)
the 5
th
and 6
th
second?
13.
A ball is thrown straight up in the air. The moment it leaves the hand of the person throwing it, it accelerates at a
rate of

9.8 m/s
2
.
a)
If the ball travels 13.3 m up than what was its initial velocity?
b)
How long does it take to reach the top of its
trajectory (13.3m)?
c)
After the ball reaches its highest point it then retur
ns to the ground with the same
acceleration,

9.8 m/s
2
.
What will its speed be when
it returns to the level of the
thrower’s hand?
14.
Running a Yellow Light
a)
A car is tr
aveling at 15 m/sec. (30 mph) on a snowy road. With a traffic light that has a "time for yellow" of 3
seconds,
how far away
from the light could the car be and get through on yellow without braking?
b)
Because of the snow, the car in problem 1
now brakes w
ith
a
n
acce
leration of

2 m/sec/sec, what time will be
required to stop the car?
c)
What will be the distance that the car travels during the time that it comes to a stop in problem #2?
d)
Between what two distances from the traffic light will
the car in t
he problems above (a, b,& c
) have no options and
run through the red light regardless of what the driver does? Explain WHY the driver will have no options!
e)
How much extra distance would a driver have to allow stopping their car if
his/her reaction time
was 0.20
seconds?
f)
Would a car traveling at 20 m/sec have any point at which it could not get through a traffic light that had a time
for yellow of 4 seconds if the road was icy and the car could only
ac
celerate at

2 m
/s
2
?
If so, what is that "no
optio
n" distance range?
15.
You throw a ball downward at a speed of 2.0m/s…
a)
What is the acceleration of the ball upon leaving your hand?
b)
How fast is the ball moving when it hits the sidewalk 2.5m below?
c)
This time you throw the ball upwards at a speed of
2.0m/s, how fast is the ball moving when it hits the
sidewalk 2.5m below?
d)
Now you just drop the ball from the same height. How fast is it moving upon hitting the sidewalk still
2.5m below?
16.
You are a hotel manager standing on the 5
th
floor when you see
a raw turkey fall past a 2.5m floor

to

ceiling
window. If the turkey is visible to you for 0.05s, what floor must it have been dropped from?
17.
An elephant shakes a tree with her trunk in order to get down some of the seed pods for food. If the lowe
st
branches of the tree are 3 m above the ground, how long does it take for the seed pods from these branches to
fall to the ground, and how fast are they falling when they do reach the ground? (Assume no air resistance)
A baby elephant catches one of t
he seed pods that fell from the top of the tree (6 m high), grabbing it with her
trunk at 1.5 m above the ground and stopping it 0.3 s later at 0.5 m above the ground; what was the seed pod’s
average acceleration between the time it was caught and the time
it was stopped?
18.
You get up at the crack of dawn one morning to go mountain biking with a friend. On a narrow downhill section
of the trail, you let her go first, since she’s eager to try out her new clipless pedals. You’re riding along at a
co
nstant velocity of 4 m/s when you turn a corner and see that your friend has stopped to watch a deer in the
woods; you don’t want to become an entangled mess of arms, legs and bike frames, so you’d like to be able to
stop before you reach her position on t
he trail, a little over 4 meters from you now. If you’re braking
acceleration on the downhill, gravel trail is 3.6 m/s
2
, can you stop in time before scaring the deer away with
your messy entanglement?
If your average velocity riding uphill on your mountai
n bike is about 5 mph, and your average velocity when
riding downhill is about 16 mph, and you spend approximately 3 hours going uphill, about how long will it take
you to ride down the mountain by the same route that you rode up?
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