Figure 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 lt 4s , 0 lt t lt 4s ` ? (b) impulse at t= 0 and t = 4 s ?
(Consider one - dimensional motion only )
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Explanation

(i) For `t lt 0 ` , the position time graph is `A_(O)` which means displacement of the particle is zero .
i.e ., particle is at rest at the origin .hence force on the particle must be zero .
For `0 lt t lt ` us , s the position time graph Ob has a constant slope . There fore , the particle remains at a distance 3m from the origin , i.e . it is at rest .. Hence froce on the particle is zero .
(iv) Impulse at t = 0
We know ,Impulse = change in linear momentum , Before t = 0 particle is at rest i.e u = 0 . After t = 0 , particle has a constant velocity `v = 3/4 `
` = 0.75 ` m/s

` :. ` impulse = `m(v-u)`
` = u (0.75 -0)`
= 3 kg m/s
Before t = 4s , ,particle has a constant velocity
u = `0.75` m/s
After t = 4s , particle is at rest i.e v= 0
Impulse = `m(v-u) = 4( 0-0.75 ) = 3 kg `m/s .