Shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for `t lt 0, t gt 4 s, 0 lt t lt 4` s ? (b) impulse at t = 0 and t = 4 s ? (Consider one­dimensional motion only).

Explanation

(a ) (i) for `lt 0` object stationary hence force acting on it during this is zero .

(ii) for `t gt 4 s` graph is parallel to time axis Hence object is stationary hence force acting on object is zero .
(iii) `0 lt t lt 4 s` During this object cover equal distance in equal time interval acting on object is zero.
( b) (i) Impulse of force at t= 0
at t=t velocity of object
`=(3)/(4) = 0.75 ms^(-1)`
= change in momentum
= mv - `mv_(0)`
`=3Ns` (ii) Impulse of force at t= 4s
At t= 4s t= 4s velocity is zero v= 0
`:. ` impulse of force
`mv - mv_(0) = m(v- v_(0))`
`=4 xx (0 - 0.75 ) = -3 Ns`