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
(a) What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
(b) What do you infer about the forces acting on the object?
(a) Here, u = 0
Using s = ut + \(\frac{1}{2}at^2\)
\(\frac{at^2}{2}\)
∴ \( a = \frac{2s}{t^2}\)
Time in seconds - Distance in metres \(a = \frac{2s}{t^2}\)
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 be increasing uniformly with time.