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.

and*a* is the rate of change of velocity.

If we reverse the differentiation by integrating in the opposite direction, we can see that Δ*v* is the time integral of *a*,

and Δ*s* 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

__s-t__ graph

- The gradient of a
*s-t* graph (at a particular instant) represents the velocity (at that instant).

__v-t__ graph

- 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).

__a-t__ graph

- The area under the
*a-t* graph (between two instants in time) represents the change in velocity (during that time interval).

Example

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.)

Solution

–

**Video Explanation **

*s-t v-t a-t* Example

### Like this:

Like Loading...

*Related*