Question

A single, non-constant force acts in the x direction on an object of mass m that is constrained to move along the x-axis. As a result the object\'s position as a function of time is:x(t)=P+Qt+Rt^3How much work is done by this force from t = 0 s to final time T? Express your answer in terms of P, Q, R, m, and T.

Answer 1

Work done is given as

`W = (1)/(2)m(2Q + 3RT^2)(3RT^2)`

Step-by-step explanation:

As we know that the position of object is given as

`x(t) = P + Qt + Rt^3`

now we know that rate of change in position of object is known as velocity

so we have

`v = (dx)/(dt)`

`v = Q + 3Rt^2`

now we have

initial speed at t = 0

`v_i = Q`

at t = T final speed is given as

`v_f = Q + 3RT^2`

now work done is change in kinetic energy

`W = (1)/(2)m(v_f^2 - v_i^2)`

`W = (1)/(2)m[(Q + 3RT^2)^2 - Q^2]`

`W = (1)/(2)m(2Q + 3RT^2)(3RT^2)`