Question

The S kg crate shown in Figure below is acted upon by a force having a...

The S kg crate shown in Figure below is acted upon by a force having a variable magnitude P = (S * t) N, where t is in seconds. Determine the crate’s velocity 4 s after P has been applied. The initial velocity is v1 = 5 m/s down the smooth plane.

s=15

Math   Statistics-And-Probability   
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Answer #1

The acceleration for the given Force is computed as:
a = F / S = t

Acceleration is the rate of change of velocity with time.

Therefore, we have here:

dV / dt = a = t

dV = t dt

Integrating from t = 0 to t = 4 on the right side and from initial speed of 5 with final speed of V, we have here:

Therefore 13 m/s is the final velocity here.

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