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Tema [17]
3 years ago
6

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 r

esult 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.
Physics
1 answer:
Serhud [2]3 years ago
7 0

Answer:

Work done is given as

W = \frac{1}{2}m(2Q + 3RT^2)(3RT^2)

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 = \frac{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 = \frac{1}{2}m(v_f^2 - v_i^2)

W = \frac{1}{2}m[(Q + 3RT^2)^2 - Q^2]

W = \frac{1}{2}m(2Q + 3RT^2)(3RT^2)

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