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The displacement of a body is given to be propotional to the cube of the time elapsed .What will be the acceleration of the body?

The displacement of a body is given to be propotional to the cube of the time elapsed.What will be the acceleration of the body?

Grade:10

1 Answers

Aarti Gupta
askIITians Faculty 300 Points
8 years ago
Suppose the displacement be taken as ‘S’ and time as ‘t’.
Now aacording to the question,
S is directly proportional to t3
Differentiating both the sides,
dS/dt directly proportional to d/dt ( t3 )
or,
dS/dt directly prop. to 3t2
Again differentiating,
d2S/dt2 directly prop. to 6t
Thus acceleration ‘a’ is directly proportional to ‘t’ (time).

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