force act on 30 gram particle in such a way that the position of particle as a function of time is given by X equals to 30 square minus 40 square + PQ where X is in metre and I is in second the work done using the first four seconds
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M = 20 gm = 0.020 kg
x = 3 t - 4 t² + t³ m
v = dx/dt = 3 - 8 t + 3 t² m/s
a = dv/dt = -8 + 6 t m/s²
Force = m a = 0.120 t - 0.160 N
Work done = dW = F dx = F * (dx/dt) * dt
dW = (0.120 t - 0.160) * (3 - 8 t + 3 t²) dt
= 0.360 t³ - 1.440 t² + 1.640 t - 0.480
W = integral of dW from t = 0 to 4 sec:
= 0.090 t⁴ - 0.490 t³ + 0.82 t² - 0.480 t ] , t = 0 to 4s
= 2.88 J
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