At time $t=0$, a particle is $20$ metres from $O$. Its velocity after $t$ seconds is \(v=3(t

Question

At time $t=0$, a particle is $20$ metres from $O$. Its velocity after $t$ seconds is $v=3(t-1)^2-12\text{ m s}^{-1}$. State the direction of motion for $0\leq t<3$ and for $t>3$.[2] Find the displacement of the particle from $O$ when $t=5$.[2] Calculate the total distance travelled in the first $5$ seconds.[3] The initial displacement from $O$ is $+20$ metres in the chosen positive direction.

Accepted Answer

(i) Negative direction for $0\leq t3$ (ii) $25\text{ m}$ (iii) $59\text{ m}$

Shifted quadratic velocity and position

Shifted quadratic velocity and position

Solution:

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