Shown the position time graph of a particle of mass 4 kg What is the force on the particle for `t lt 0 , 0 lt t lt4 s` motion only
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Explanation

(a) (i) for `t lt 0` the position time graph is AO which means displacement of the particle must be zero
(ii) for `0 lt t lt 4 s` the position time graph OB has a constant slope Therefore velocity of the particle is constant in this interval i.e particle has zero acceleration Hence force on the particle must be zero
(iii) For `t gt 4 s` the position time graph BC is parallel to time axis Therefore the particle remains at a distance of 3 m from the origin i.e., it is at rest Hence force on the particle is zero
(b) 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 `upsilon = (3)/(4) = 0.75 m//s `
`:.` Impulse ` = m (upsilon - u ) = 4 (0.75 - 0) = 3 kg ms^(-1)`
Impulse at `t = 4 s `
Before t = 4 s particle has a constant velocity `u = 0 .75 m//s `
After t = 4 s particle is at rest i.e., `upsilon = 0`
`:.` Impulse ` = m (upsilon - u ) = 4 (0 - 0 .7 5 ) = -3 kg ms^(-1)`.