Question

A particle, of mass 200g, is initially moving with a speed of 15 ms^-1, along the X–axis. It is acted upon by a force that remains directed along the X–axis but whose magnitude varies with time in the manner shown. The final speed of the particle, at t = 20s, would be

(1) 160 ms^-1

(2) 165 ms^-1

(3) 180 ms^-1

(4) 185 ms^-1

Answer 1

(4) 185 ms^-1

We known that F = dp/dt

The integral, on the left, representing impulse, equals the area under the F vs t graph. From the given figure, this area is

∴ Change in momentum = 34 N-s

∴ Final momentum, after 20 s = (200/1000 x 15 + 34)N - s

= 37 (N–s)

∴ Final speed of the ball = (37/200/1000)ms^-1

= 185 ms^-1