A crate on a motorized cart starts from rest and moves with a constant eastward acceleration ofa= 2.60 m/s^2. A worker assists t

Question

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A crate on a motorized cart starts from rest and moves with a constant eastward acceleration ofa= 2.60 m/s^2. A worker assists t

he cart by pushing on the crate with a force that is eastward andhas magnitude that depends on time. According to F(t) = (5.40 N/s)t. What is the instantaneouspower supplied by this force at t= 4.70 s

Physics

1 answer:

Keith_Richards [3.2K] · Answer 1 · 2026-04-01T16:46:06+03:00

Response:

To find power, we must first determine the work done by the force.

1) We will use the following equation to calculate work:

$\int\limits {F} \, dx$

The force is provided by the problem; our goal is to express 'dx' in terms of 't'

2) It's known that:

$\frac{dV}{dt} = a = 2.6$

Thus, we have:

$v = 2.6t$

Then:

$\frac{dx}{dt} = V = 2.6t\\ \\dx = 2.6t*dt$

3) Finally, substituting all known values gives us:

$\int\limits^{4.7}_{0} {5.4t*2.6t} \, dt$

After some calculations, the resulting work is:

161.9638 J.

4) To find power, we will use the following equation:

$P = \frac{W}{t}$

Thus

P = 161.9638/4.7 = 34.46 W