Review  One Dimensional Motion


1.

A fast sprinter can cover 100 m
in 10 s flat. (a) What is the average speed of the sprinter?
(b) What would his time be for the mile (1610 m) if
he could keep up the sprint pace?


2.

If y = kx, where k is a constant,
what is the effect on y: of (a) doubling x, (b) of halving
x? (c) What does a graph of y as a function of x look
like?


3.

If y = kx^{2},
where k is a constant, what is the effect on y: of (a)
doubling x, (b) of halving x? (c) What does a graph
of y as a function: of (i) x and (ii) x^{2}
look like?


4.

An object moves with a constant
velocity of 15 m/s. (a) How far will it travel in 2.0
s? (b) If the time is doubled, how far will it travel?


5.

An object, initially at rest, moves
with a constant acceleration of 10 m/s^{2}.
How far will it travel in (a) 2.0 s and (b) 4.0 s? If
this object had an initial velocity of 4 m/s, how far
will it travel in (c) 2.0 s and (d) 4.0 s?


6. 
(a) An object moving with constant
acceleration changes its speed from 20 m/s to 60 m/s
in 2.0 s. What is the acceleration? (b) How far did
it move in this time?


7. 
The speed of light is 3.0 x 10^{8}
m/s. Assume that the length of a "standard room"
is 20 m (22 yards). How many "room lengths"
can light travel in 20/3 s?


8. 
A pitcher throws a baseball with
a velocity of 132 ft/s (90 mph) toward home plate that
is approximately 60 ft away. Assuming the horizontal
velocity of the ball remains constant, how long does
it take to reach the plate?


9. 
An object moving with constant
acceleration along a horizontal path covers the distance
between two points 60 m apart in 6.0 s. Its speed as
it passes the second point is 15 m/s. Find (a) the speed
at the first point, (b) its acceleration and (c) the
initial distance from the first point when the object
was at rest.


10. 
Figure 1 is a plot of the displacement
x of an object as a function of time t. The dashed vertical
lines separate the onesecond intervals. During the first
time interval (#1 or t = 0 to t = 1 s) of Fig. 1 decide if
the velocity of the object is (a) zero (b) constant and
positive, (c) constant and negative, (d) increasing and positive,
(e) increasing and negative, (f) decreasing and positive,
or (g) decreasing and negative. (You may use a ruler to check
the slopes of x vs t for the various time intervals.) Also
decide for the same intervals if the acceleration is (note
do not fix on one point in an interval) (h) positive (i) negative
(j) zero. Explain your answers. Repeat the above for the other
four time intervals in Fig. 1.



11. 
A car is traveling along a straight
level road at a speed of 80 ft/s (54.5 mph). The brakes
of the car are capable of producing a negative acceleration
of 20 ft/s^{2}. (a) How long
will it take the car to stop? (b) How far will the car
travel in this time? (c) Now assume that it takes one
and onehalf second for the driver of the car to become
aware of the need to stop and another halfsecond before
her brakes take hold. How far will the car travel before
it comes to a stop if we assume, as before that she
was initially traveling with a speed of 80 ft/s? (d)
If we take 15 ft as the length of the car, how many
"car lengths" will the car travel in (c) before
coming to a halt?


12. 
In Fig. 2 at t = 1.0 s, the velocity
of the particle is +15 m/s. At t = 5.0 s, the velocity
of the particle is 15 m/s. Are (a) the magnitudes of
the velocity at these two times equal? (b) The directions
of the velocity at these twotime the same?


13. 
Figure 2 shows the velocity of
a particle as a function of time. (a) Find the acceleration
for the five onesecond periods and plot the acceleration
as a function of time. (b) Taking x = 0 at t = 0, find
the position of the particle at t = 0.5 s, t = 1.0 s,
t = 2.0 s, t = 3.0 s, t = 4.0 s, and t = 5.0 s and plot
the position as a function of time. Look at the slopes
of your x vs t curve for the five onesecond periods
and show that they correspond to the velocities of Fig.
2.



14.

A ball thrown straight up takes
2.0 s to reach a height of 40 m. Find (a) Its initial
speed, (b) its speed at this height, and (c) how much
higher the ball will go. Take g = 10 m/s^{2}.


15.

A ball is thrown down vertically
with an initial speed of 20 m/s from a height of 60
m. Find (a) its speed just before it strikes the ground
and (b) how long it takes for the ball to reach the
ground. Repeat (a) and (b) for the ball thrown directly
up from the same height and with the same initial speed.
Take g = 10 m/s^{2}.


16.

An object moving with a velocity
of 10 m/s is uniformly decelerated, coming to rest in
a distance of 20 m. Find (a) its deceleration and (b)
the time for it to come to rest. Plot (c) its velocity
v as a function of time t and (d) its position x as
a function of t. Take x_{o} =
10 m.


17.

An apartment dweller sees a flowerpot
(originally on a windowsill above) pass the 2.0mhigh
window of her fifth floor apartment in 0.10 s. The distance
between floors is 4.0 m. From which floor did the pot
fall?


18.

At a certain instant, a ball is
thrown downward with a velocity of 8.0 m/s from a height
of 40 m. At the same instant, another ball is thrown
upward from ground level directly in line with the first
ball with a velocity of 12 m/s. Find (a) the time when
the balls collide, (b) the height at which they collide
and (c) the direction the second ball is traveling when
they collide. Take g = 10 m/s^{2}.


19.

Sketch a graph that is a possible description
of position as a function of time for a particle that moves
along the x axis and, at t = 1 s, has (a) zero velocity and
positive acceleration; (b) zero velocity and negative acceleration;
(c) negative velocity and positive acceleration; (d) negative
velocity and negative acceleration. (e) For which of these
situations is the speed of the particle increasing at t =
1 s?

