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Figure shows the position-time graph of a particle of mass 4 kg, then 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 one-dimensional motion only) |
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Answer» Solution : i) For `t lt 0`in the position time graph is at 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 II) For 0 < t < 4 s, the position time graph OA 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 > 4 s, the position time graph AB is parallel to time AXIS. Therefore, the particle remains at a distance 3M from the origin, i.e. it is at rest. Hence force on the particle is zero. B)i) 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` `therefore` Impulse `=m(v-u) =m(0.75 -0) = 3` kgm//s (ii) `therefore`Impulse at t = 4 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 |
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