Video Transcript
The figure shown is a
velocity–time graph for a body moving in a straight line. Determine the deceleration of
the body during the final section of its movement, given that it came to rest
100 seconds after it started moving.
We know that the acceleration
on a velocity–time graph is equal to its slope or gradient. We can therefore calculate the
acceleration at any point by dividing the change in velocity by the change in
time. In this question, our velocity
is measured in meters per second, and our time is measured in seconds. Dividing meters per second by
seconds gives us meters per second per second. This is written as meters per
second squared or meters per square second.
When the slope or gradient of
our graph is positive, the body will be accelerating. When the slope or gradient of
the graph is negative, the body will be decelerating. Finally, if a line on our
velocity–time graph is horizontal, the acceleration will be equal to zero and
the body will be traveling with a constant velocity. In this question, we’re
interested in the deceleration in the final section of the graph. This occurs between 90 seconds
and 100 seconds. The velocity during this time
period has decreased from 45 meters per second to zero meters per second. This means that our change in
velocity is zero minus 45.
As mentioned, the time period
goes from 90 seconds to 100 seconds. Therefore, the change in time
is 100 minus 90. This can be simplified to
negative 45 over 10. When dividing by 10, we move
all our digits one place to the right. And dividing a negative number
by a positive gives a negative answer. The acceleration of the body is
therefore negative 4.5 meters per square second. The deceleration will be the
absolute value or modulus of this. This is equal to 4.5 meters per
square second.
