A particle moves in a straight line so that, $t$ seconds after passing through a fixed point $O$

Question

A particle moves in a straight line so that, $t$ seconds after passing through a fixed point $O$, its velocity $v$ ms${}^{-1}$, is given by $v=3e^t-40e^{-2t}$. Find the initial velocity of the particle. the value of $t$ when the particle is instantaneously at rest. the acceleration of the particle when $t=\ln 2$. the value of $t$ when the acceleration is minimum. an expression for the displacement in terms of $t$.

Accepted Answer

(a) $-37\text{ m s}^{-1}$. (b) $t=\frac13\ln\frac{40}{3}=0.863$ s. (c) $26\text{ m s}^{-2}$. (d) Minimum acceleration at $t=\frac13\ln\frac{160}{3}=1.33$ s. (e) $s=3e^t+20e^{-2t}-23$.

Kinematics - Maximum and Minimum Motion Quantities

Kinematics - Maximum and Minimum Motion Quantities

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