Distance moved by a body is α t3
, where ‘t’ is the time, What conclusion do you draw about
acceleration. Is it constant or increasing or decreasing or zero?
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Answer:
According to the data given, we conclude that the distance covered by an object is directly proportional to the cube of time taken.
∴ x∝t
3
⟹x=kt
3
where k is constant
Differentiating w.r.t time,
dt
dx
=k(3t
2
)
Differentiating again w.r.t time,
dt
2
d
2
x
=
dt
d
(3kt
2
)=6kt
⟹ Acceleration of the object
dt
2
d
2
x
=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.
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