Question

The following is the distance-time table of an object in motion:

Time in seconds	Distance in metres
0	0
1	1
2	8
3	27
4	64
5	125
6	216
7	343

1. What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
2. What do you infer about the forces acting on the object?

Answer 1

a) Here, u = 0

Using s = `ut + 1/2 at^2`

= `(at^2)/2`

∴ a = `(2s)/t^2`

Time in Seconds	Distance in metres	`a = (2s)/t^2`
0	0	0
1	1	2
2	8	4
3	27	6
4	64	8
5	125	10
6	216	12
7	343	14

Thus, acceleration is increasing.

b) As F = ma, therefore, F ∝ a. Hence, the force must also increase uniformly with time.