The time rate of work being done or energy transfer is defined as Power.
Instantaneous Power delivered = dW/dt = F * v * cos Ө
W is the work done by force F, t is time instant, v is velocity of the particle and Ө is the angle between Force and velocity.
Average Power delivered in Δt time interval = ΔW/Δt
Q.1 A body of mass m1 accelerates uniformly from rest to v1 in time t1, the instantaneous power delivered to the body as a function of time ‘t’ is
(a) m* v1* t / t1 (b) m * v12 * t / t12 (c) m * v1 * t2 / t1 (d) m * v12 * t / t1
Q.2 A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ‘t’ is proportional to (a) t0.75 (b) t1.5 (c) t0.25 (d) t0.5
Q.3 A 70 Kg man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force F to raise himself. The centre of gravity rises by 0.5 before he leaps. After the leap the C.G. rises by another 1m. The maximum power delivered by the muscles is: (Take g = 10 m/s2)
(a) 6.26 * 103 W at start (b) 6.26 * 103 W at take-off (c) 6.26 * 104 W at start (d) 6.26 * 104 W at take off
Q.4 Two bodies of equal masses are dropped on a planet from two different heights ‘a’ and ‘b’ above ground (a > b). The average power delivered by gravity to the two masses in the last second of motion are Pa and Pb, then (Assuming that both the masses travel for more than 1 second and neglecting air resistance):
(A) Pa > Pb (B) Pb > Pa (C) Pa = Pb (D) None