Question

if the velocity of an object is reduced to half:find the change in:- i) initial and final velocity. ii) change in momentum. iii) rate of change in momentum

Answer 1

Dear student,

Let a body of mass m and velocity v is brought to rest in time t.

Initial momentum = mv

Final momentum = m × 0 = 0 ( as the object is brought to test its velocity is zero)

Change in momentum = final momentum - initial momentum= 0 - mv

Time in which object is brought to rest = t

Rate of change in momentum = - mv/t

Force F = Rate of change of momentum = - mv/t

Impulse = Force F × t = change in momentum = -mv

When the time in which the object is brought to rest, there is no change in,

Initial momentum, it remains mv
Final momentum, it remains zero
Change in momentum, it remains -mv.
The only change is in the rate of change of momentum, which is doubled when the time is halved.
Though impulse (=change in momentum) does not change, the force required is doubled.

Regards,