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The position of a particle is given by v...

The position of a particle is given by `vecr=(8thati+3t^(2)hatj+5hatk)m` where t is measured in second and `vecr` in meter. Calculate, the velocity and the acceleration of the particle.

Text Solution

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Here `vecr =(8t hati +3t^(2) +5 hatk)m`
Velocity of a particle is given by `v=(dr^(rarr))/(dt)`
`v=(d)/(dt) 8(t hati +3 t^(2) hatj +5 hatk) =8 hati +6t hat j+0=(8 hati+6t hatj)" ms"^(-1)" …(i)"`
Acceleration of a particle is given by `a=(dv)/(dt)`
`a=(d)/(dt) 8 (hati +6t hatj) =0+6 hatj =(6 hatj)" ms"^(-2)" ....(ii)"`
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