A particle moves in a straight line with acceleration $a=(6t-12)\text{ m s}^{-2}$, where $t$ is

Question

A particle moves in a straight line with acceleration $a=(6t-12)\text{ m s}^{-2}$, where $t$ is the time in seconds. Initially, its velocity is $18\text{ m s}^{-1}$ and its displacement from $O$ is $-4$ metres. (i) Find the velocity of the particle in terms of $t$. (ii) Show that the particle is never instantaneously at rest, and find its minimum speed. (iii) Calculate the distance travelled in the first $5$ seconds.

Accepted Answer

(i) $v=3t^2-12t+18\text{ m s}^{-1}$ (ii) Minimum speed $6\text{ m s}^{-1}$ at $t=2\text{ s}$, never at rest (iii) $65\text{ m}$

Acceleration with a positive minimum speed

Acceleration with a positive minimum speed

Solution:

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