A particle travelling in a straight line starts from rest at point $O$ and has acceleration (in \(

Question

A particle travelling in a straight line starts from rest at point $O$ and has acceleration (in $\text{m s}^{-2}$)
Modelled by the equation $a = 12 - 8t$, where $t$ is measured in seconds.

Find an expression for the velocity of the particle at time $t$.
Find an expression for the position of the particle at time $t$.
Find its furthest distance from $O$ in a positive direction during the subsequent motion.
Find the time taken for the particle to return to $O$, and its velocity at that time.
Describe the motion of the particle after it passes through $O$ for the second time.

Accepted Answer

(a) $v=12t-4t^2\text{ m s}^{-1}$; (b) $s=6t^2-\dfrac43t^3\text{ m}$; (c) $18\text{ m}$; (d) $t=\dfrac92\text{ s}$, $v=-27\text{ m s}^{-1}$; (e) continues in the negative direction with increasing speed

Kinematics - Speeding Up and Slowing Down

Kinematics - Speeding Up and Slowing Down

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