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A) A bus starts from the stop and takes 50sec to get the speed of 10m/s.If the mass of the bus along with the passengers is 10000kg, calculate the force applied by the engine of bus to push the bus at a speed of 10m/s. b) A vehicle having mass equal to 1000kg is running with a speed of 10m/s.After applying the force of 1000N for 10sec. what will happen to the speed of the vehicle? c)Find the recoil velocity of a gun having mass equal to 8kg, if a bullet of 25gm aquires the velocity of 400m/s after firing from the gun. d)A girl of 30kg mass is running with a velocity of 2m/s.She jumps over a stationary cart of 3kg while running.Find the velocity of the cart after jumping of boy.

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A) v = u + a t u = 0 , t = 50 sec. v = 10 m/s => a = 10/50 = 0.20 m/s² Force = F = m a = 10, 000 * 0.20 = 2, 000 Newtons = 2, 000 kN

Force can also be calculated as the rate of change of momentum of the bus: = [ 10, 000 * 10 - 10, 000 * 0 ] / 50 = 2000 kN

B)

F = 1, 000 N and m = 1,000 kg => a = F/m = 1 m/s²

u = 10 m/s t = 10 s v = u + a t = 10 + 1 * 10 = 20 m/s

c) We apply the conservation of momentum principle. m1 = 8 kg, v1 = ? m2 = 25 gm and v2 = 400 m/s m1 v1 + m2 v2 = 0 v1 = - 0.025 * 400 / 8 = -1.25 m/s the gun recoils with 1.25 m/s

d) we apply the principle of conservation of momentum. we ignore the friction between the cart and the ground as well as between the girl and the ground..

m1 = 30 kg m2 = 3 kg v1 = 2 m/s v2 = 0

m1 v1 + m2 v2 = (m1 + m2) v 30 kg * 2 m/s + 3 kg * 0 = (33) * v v = 20/11 m/sec both the cart and the girl move together with this velocity after the girl jumps on to the cart.