On a velocity vs. time graph, how do you show acceleration?

Question

Would acceleration be a curve, or a straight line?

Some info from the problem:
Object is accelerating, starting from rest
Accelerates for 4 seconds
Changes position from 2m to 10m

So, how would you find acceleration and then how would you show this on a velocity vs. time graph

Thanks!

Answer 1

On a velocity vs time graph, constant acceleration is shown as a straight line, with slope equal to rate of acceleration. If, say that constant acceleration is 0.0, then the line will be horizontal (slope = 0).

In your example :
Average velocity = (10m - 2m) / 4s = 8m / 4s = 2m/s
Assuming constant acceleration, final velocity = 2 * 2m/s = 4m/s
Acceleration = (4m/s) / 4s = 1 m/s^2

This would be shown on a graph as a line going through (0,0) and (4,4) with the axes labeled in m/s and s.

Answer 2

Take the derivative of the velocity function with respect to time.