Exponential velocity to instantaneous rest
Exponential velocity to instantaneous rest
Secondary 4
6 marks
Original parallel to supplied A Math Kinematics references
A particle passes through \(O\) at time \(t=0\). Its velocity at time \(t\) seconds is \(v=(15\mathrm{e}^{-t/3}-3)\text{ m s}^{-1}\), where \(t\geq0\).
- Find the acceleration of the particle.[1]
- Find the exact time at which the particle first comes to rest.[2]
- Calculate the distance travelled before it first comes to rest.[3]
Solution:
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Answer:(i) \(a=-5\mathrm e^{-t/3}\text{ m s}^{-2}\) (ii) \(t=3\ln5\text{ s}\) (iii) \(36-9\ln5\text{ m}\)
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