At time $t=0$, a particle is at rest at a point $10$ metres from $O$. Its acceleration after \

Question

At time $t=0$, a particle is at rest at a point $10$ metres from $O$. Its acceleration after $t$ seconds is $a=(12-6t)\text{ m s}^{-2}$, where $0\leq t\leq6$. Find the velocity of the particle in terms of $t$.[2] Find the positive time at which the particle is next instantaneously at rest.[1] Find the greatest displacement of the particle from $O$.[2] Calculate the total distance travelled in the first $6$ seconds.[3] The initial displacement from $O$ is $+10$ metres in the chosen positive direction.

Accepted Answer

(i) $v=12t-3t^2\text{ m s}^{-1}$ (ii) $t=4\text{ s}$ (iii) $42\text{ m}$ (iv) $64\text{ m}$

Linear acceleration and a return to the starting point

Linear acceleration and a return to the starting point

Solution:

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