A partical of mass `m` is driven by a machine that deleveres a constant power `k` watts. If the partical starts from rest the force on the partical at time `t` is

Options

A. `sqrt2mk t^(-1/2)`
B. `1/2 sqrt mk t^(-1/2)`
C. `sqrt(mk/2)t ^(-1/2)`
D. `sqrt mk t^(-1/2)`

Answer

`(3)`

Explanation

Constant power acting on the particle of mass m is k watt. Or P = K
`(dW)/dt = k, dW = kdt`
Integrating both sides, `int _(0)^(w) dW = int _(0)^(t) kdt `
`Rightarrow W = kt ---(i)`
Using work energy theorem,
`W = 1/2 mv^(2) - 1/2 m(0)^(2)`
`kt = 1/2 mv^(2) "[using equation(i)]"`
`v = sqrt((2kt)/(m))`
Acceleration of the particle, `a = dv/dt`
` a = 1/2sqrt(2k)/(m) 1/ sqrt2 = sqrt (k)/(2mt)`
Force on the particle,
`F = ma = sqrt(mk)/(2t) = sqrt((mk)/(2)) t^(-1/2)`