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A mass m starts from rest and is brought to speed v with constant acceleration over a time interval T. The instantaneous power supplied to the body at time t is

1. (mv²)/(T²) t²
2. (mv²)/(T²) t
3. (1)/(2)(mv²)/(T²) t²
4. (1)/(2)(mv²)/(T²) t

Correct answer: (mv²)/(T²) t

Solution

Constant acceleration a = v/T, so velocity at time t is v(t)=vt/T and force F=ma=mv/T. Instantaneous power P = F*v(t) = (mv/T)(vt/T) = m v^2 t / T^2.

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