Motion in One Dimension
False. The car may be slowing down, so that the direction of its acceleration is
opposite the direction of its velocity.
True. If the velocity is in the direction chosen as negative, a positive acceleration
causes a decrease in speed.
True. For an accelerating particle to stop at all, the velocity and acceleration must
have opposite signs, so that the speed is decreasing. If this is the case, the particle will
eventually come to rest. If the acceleration remains constant, however, the particle
must begin to move again, opposite to the direction of its original velocity. If the
particle comes to rest and then stays at rest, the acceleration has become zero at the
moment the motion stops. This is the case for a braking car—the acceleration is
negative and goes to zero as the car comes to rest.
The velocity-vs.-time graph (a) has a constant slope, indicating a constant acceleration,
which is represented by the acceleration-vs.-time graph (e).
Graph (b) represents an object whose speed always increases, and does so at an ever
increasing rate. Thus, the acceleration must be increasing, and the acceleration-vs.-time
graph that best indicates this behavior is (d).
Graph (c) depicts an object which first has a velocity that increases at a constant rate,
which means that the object’s acceleration is constant. The motion then changes to one at
constant speed, indicating that the acceleration of the object becomes zero. Thus, the best
to this situation is graph (f).
(b). According to
, there are some instants in time when the object is simultaneously
at two different x-coordinates. This is physically impossible.
of Figure 2.14b best shows the puck’s position as a function of time. As
seen in Figure 2.14a, the distance the puck has traveled grows at an increasing rate for
approximately three time intervals, grows at a steady rate for about four time
intervals, and then grows at a diminishing rate for the last two intervals.
of Figure 2.14c best illustrates the speed (distance traveled per time
interval) of the puck as a function of time. It shows the puck gaining speed for
approximately three time intervals, moving at constant speed for about four time
intervals, then slowing to rest during the last two intervals.