The variation with time of a, v and s for a rectilinear motion are often plotted on graphs. The resulting graphs are called the a-t, v-t and s-t graphs respectively.
Remember that v is the rate of change of displacement.
anda is the rate of change of velocity.
If we reverse the differentiation by integrating in the opposite direction, we can see that Δv is the time integral of a,
and Δs is the time integral of v.
Never mind the calculus if it intimidates you. The A-level only tests these concepts graphically. All you need to know is that
- The gradient of a s-t graph (at a particular instant) represents the velocity (at that instant).
- The gradient of a v-t graph (at a particular instant) represents the acceleration (at that instant).
- The area under the v-t graph (between two instants in time) represents the change in displacement (during that time interval).
- The area under the a-t graph (between two instants in time) represents the change in velocity (during that time interval).
Given the v-t graph for the motion of a ball over 5 seconds, derive the corresponding s-t and a-t graphs. (Assume “rightward is positive” sign convention.)