Describe in words the motion plotted in Fig. 2-32 in terms of velocity, acceleration, etc. [Hint: First try to duplicate the motion plotted by walking or moving your hand.]

Velocity is a vector quantity and is defined as the rate of change of displacement of an object with time. Its unit of measurement $\mathrm{m}/\mathrm{s}$.

Acceleration is the time rate of change of velocity. Its unit of measurement is $\mathrm{m}/{\mathrm{s}}^2$.

The slope measures the steepness of a line. It is defined as the ratio of change in the y-coordinate to that in the x-coordinate.

The slope of a position (displacement)-time graph is equal to the velocity over that time interval. The steeper the slope of the given curve is, the greater is the velocity.

The given graph represents the motion as displacement over time. The object starts from rest, i.e., at the origin $\left(x=0\right)$with a constant velocity and zero acceleration.

At about $t=17\mathrm{s}$, the object has covered a 5-m distance. It gains velocity till $t=20\mathrm{s}$. For the next 10 seconds $\left(t=30\mathrm{s}\right)$, the positive curve indicates an increase in velocity and positive acceleration.

From $t=30\mathrm{s}$to $t=45\mathrm{s}$, the object instantaneously slows down to rest, reverses its direction of motion, and speeds up again to move backward. Here, the object decelerates.

For the last five seconds, from $t=45\mathrm{s}$to $t=50\mathrm{s}$, the object motion is still along the negative direction but at a slow speed. It gives a positive acceleration. The object finally stops at $t=50\mathrm{s}$and is 10 m away from its starting point.