A rocket-propelled sled of mass is released from rest on a straight

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A rocket-propelled sled of mass

5\,\text{kg}

is released from rest on a straight, horizontal, frictionless track at position

x = 0

. The thrust acting on the sled is horizontal and varies with displacement according to

F(x) = 40 + 2x

newtons, where

x

is the displacement in metres measured from the starting point. (i) Establish the differential equation that connects the sled’s velocity

v

and displacement

x

under the given force law. (ii) Integrate this equation to obtain

v

as a function of

x

and hence write the explicit expression for

v(x)

. (iii) Compute the velocity of the sled after it has travelled

10\,\text{m}

. (iv) Determine the time taken by the sled to cover the first

10\,\text{m}