Exponential velocity and turning point
Exponential velocity and turning point
Secondary 4
7 marks
Original parallel to supplied A Math Kinematics references
A particle passes through \(O\) at time \(t=0\) with velocity \(v=(8\mathrm{e}^{-t/2}-2)\text{ m s}^{-1}\), where \(t\geq0\).
- Find the acceleration of the particle and explain why its velocity is decreasing.[2]
- Find the exact time at which the particle is instantaneously at rest.[2]
- Calculate the distance travelled from \(O\) before the particle first comes to rest.[3]
Solution:
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Answer:(i) \(a=-4\mathrm e^{-t/2}\text{ m s}^{-2}\), so velocity decreases (ii) \(t=4\ln2\text{ s}\) (iii) \(12-8\ln2\text{ m}\)
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