The following is the distance-times 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?

According to the data given, we conclude that the distance covered by an object is directly proportional to the cube of time taken.
∴x∝t³
⇒x=kt³
where k is constant
Differentiating w.r.t time,
dx/dt=k(3t²)
Differentiating again w.r.t time,
d²x/dt²=d/dt(3kt²)=6kt
⇒Acceleration of the object d²x/dt²=a=6kt
Hence, the acceleration of the object is not constant and increases with time.
Force acting on the object
F=ma=m(6kt)
⇒F=6kmt
i.e force acting on the object increases with time.