Question:
Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t1 as a function of time t is given by
Answer:
W = F × s
and
F = m × a
so
W = m × a × s
"The body is accelerated from 0 to v in time tâ‚"
so
v = 0 + a × tâ‚
a = v / tâ‚
The distance traveled in a certain time t is W = m × (v / tâ‚) × ( (v × t²) / (2 × tâ‚) )
Rearranging the equation,
W = (m × v² × t²) / (2 × t₲)
Or, W = ( m × v² / 2 ) × ( t / tâ‚ )²
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