A particle is projected vertically upwards with a velocity of 196 m/sec. What will be its velocity at the end of 30 seconds?

A particle is projected vertically upwards with a velocity of 196 m/sec. What will be its velocity at the end of 30 seconds? Correct Answer 98 m/sec in the downward direction

Let the particle projected from A with velocity u = 196 m/sec and P be its position at time t where, AP = x m, if v m/sec be its velocity at P,then the equation of motion of the particle is, dv/dt = -g ……….(1) Since v = u, when t = 0, hence from (1) we get, u∫vdv = -g 0∫tdt Or v – u = -gt Or dx/dt = u – gt ……….(2) Let v1 be the velocities of the particle after 10 seconds from the instant of projection. Then v = v1 when t = 10; hence from (2) we get, v1 = 196 – (9.8)*30 = -98 m/sec Since the upward direction is taken as positive, hence after 30 seconds the velocity of the particle is -98 m/sec in the upward direction. So, the velocity will be 98 m/sec in the downward direction.