Practice Questions for Test I
I. Horizontal Linear Motion
v= d/ t(constant speed)
a=(vf - vi) / t
vf = vi + at
d= vi t + (½)at2
2ad= vf 2 – vi 2
1. A toy wagon rolls down an inclined plane with constant acceleration. It starts from rest and attains a speed of
6m/s in 1s. Find the acceleration and the distance moved during that period.
Ans) a=6m/s2, d=3m
2. A runner is running at a constant speed of 6m/s. The runner gets tired and slows down to a speed of 2m/s in 2
seconds. What is the acceleration of the runner?
Ans) a= -2m/s2
3. A motorcycle, starting from rest, has an acceleration of 5m/s 2. What is the speed of the motorcycle when it moved
a distance of 10 meters?
Ans) v=10m/s
4. The length of the tunnel is 20 meters. A bicycle enters the tunnel at a speed of 3m/s and leaves the tunnel at 2m/s.
How long did it take for the bicycle to go through the tunnel?
Ans) a= -0.125m/s2 , t=8s
5. A jet plane lands with a speed of 100m/s and can accelerate at a maximum rate of -5m/s² as it comes to rest. (a)
From the instant the plane touches the runway, what is the time it needs before it can come to rest? (b) Can this
plane land at a small tropical island airport where the runway is 800m? Explain
Ans) t=20s , d=1000m(can’t land)
6. A truck on a straight road starts from rest, accelerating at 2m/s2 until it reaches a speed of 20m/s. Then the truck
travels for 20s at constant speed until the brakes are applied, stopping the truck for an additional 5s. Find the total
distance traveled the truck during this motion.
Ans) d=550m
v= d/ t(constant speed)
a=(vf - vi) / t
d= vi t + (½)at2
vf = vi + at
2ad= vf 2 – vi 2
7. A car is traveling on a dry road with a speed of 32m/s. The driver slams on the brakes and skids to a halt with an
acceleration of -8m/s2. On an icy road, the car would have skidded to a halt with an acceleration of -3m/s2. How
much farther would the car have skidded on the icy road compared to the dry to the dry road?
Ans) 106.7m further on icy road~
8. A rocket-propelled car starts from rest and moves in a straight line with a=5m/s² for 8 seconds until the fuel is
exhausted. It then continues with constant velocity. What distance does the rocket-car cover in 14 seconds?( *~ That
is, 8s when accelerating, then moves 6s more with constant speed, in total 14s)
Ans) 400m
9. A cheetah is walking at a speed of 1.1m/s when it observes a rabbit 41m directly ahead. If the cheetah accelerates
at 9.55m/s2, how long does it take the cheetah to reach the rabbit if the rabbit doesn’t move?
( you may have to use the quadratic formula; when ax 2 + bx +c =0, then x =
√
)
Ans) t=2.82s
4. The following x-t graph displays
the motion of a car moving in
straight line. Answer the questions
below
i) When is the speed of the car
increasing?
Ans) CD
x(m)
slopes are decreasing
(v is decreasing)
ii) When is the speed of the car
decreasing?
Ans) BC
Slope is linear
(v=const.)
slopes are increasing
(v is increasing)
B
no change in position though time
D
E
F
A
0
iii) When does the car reverse direction?
Ans) C
iv) When is the car moving at a constant speed?
Ans) AB
v) When does the car stay motionless?
Ans) EF and beyond
C
t(s)
II. Vertical Linear Motion(Free-fall)
vf = vi - gt, y= vit - (½)gt2 , -2gy = vf 2 – vi 2 , g=9.8m/s2
1. A body falls freely from rest. i) Find the distance it falls in 5 seconds, ii) the velocity after falling 66m.
Ans) y= -122.5m , v= -36m/s
2. In a football game, the referee tosses a coin up with an initial speed of 4m/s. How high does the coin go above its
point of release? What is the total time the coin is in the air before returning to its release point?
Ans) y=0.82m , t=0.81s
3. A ball thrown vertically upward returns to its starting point in 8 seconds. Find its initial velocity.
Ans) v=39.2m/s
4. A stone is thrown downward with an initial velocity of -5m/s from a height of 15 meters. Find the velocity with
which it strikes the ground and time it takes to reach the ground.
Ans) v= -17.9m/s , t=1.32s
6. A baseball is thrown straight upward with a velocity of 20m/s. How long will it take to reach the maximum
height? How high will it rise? How long will it take to return to the starting point?
Ans) t=2.04s , y=20.41m , t=0.408s
Additional Questions
1. A car is accelerating as it passes two checkpoints that are 40m apart. The time taken between checkpoints is 6
seconds and the car’s speed at the first checkpoint is 5m/s. Find the car’s acceleration and its speed at the second
checkpoint.
Ans) a=0.56m/s2 , v=8.36m/s
2. Two clumsy boys are running toward each other. When they are 100m apart they are running at a constant speed.
One runs with a constant speed of 5m/s, while the other moves at 7m/s. How close are they to the slower one’s
initial point(when they are 100m apart) when they collide with each other? (In other words, the distance from the
slower ones initial point to the collision point)
Ans) 41.7m
vf = vi - gt, y= vit - (½)gt2 , -2gy = vf 2 – vi 2 , g=9.8m/s2
3. The acceleration due to gravity on the moon is 1.67m/s². If a person can throw a stone 15m straight upward on the
earth, how high should the person be able to throw a stone on the moon? Assume that the throwing speeds are the
same in the two cases. (remember that gearth=9.8m/s2, gmoon=1.67m/s2)
Ans) y=88.1m on the moon
4. A stone is thrown vertically upward with velocity 40m/s at the edge of a cliff having a height of 110
meters. i) Find the maximum height the stone will rise. ii) From the origin(=cliff), find the position of the
stone at t=1s, t=3s, t=7s, t=8s and t=9s.
Ans) y=81.6m(from the release point),
y=35.1m at t=1s, y=75.9m at t=3s,
y=6.4m at t=8s, y= -36.9m at t=9s
y=39.9m at t=7s
5. An antiaircraft shell is fired vertically upward with an initial velocity of 500m/s. Compute i) the maximum height
it can reach, ii) the time taken to reach the maximum height, iii) the instantaneous velocity at the end of 60s and
determine if it is on its way up or down at that speed. iv) When will its height be 10,000m? If you get two answers,
explain why.
(use quadratic formula : if ax2+bx –c=0, then x =
Ans) i) y=12755m
√
)
ii) t=51s iii) -88m/s(down) iv) t=27.3s(going up) and t=75s(going down)