A particle passes through $O$ at time $t=0$. Its velocity after $t$ seconds is \(v=\dfrac{12t}

Question

A particle passes through $O$ at time $t=0$. Its velocity after $t$ seconds is $v=\dfrac{12t}{(t+1)^2}\text{ m s}^{-1}$, where $t\geq0$. (i) Show that the acceleration is $\dfrac{12(1-t)}{(t+1)^3}\text{ m s}^{-2}$. (ii) Find the maximum speed of the particle and the time at which it occurs. (iii) Find the displacement of the particle from $O$ when $t=3$.

Accepted Answer

(i) $a=\dfrac{12(1-t)}{(t+1)^3}\text{ m s}^{-2}$ (ii) $3\text{ m s}^{-1}$ at $t=1\text{ s}$ (iii) $12\ln4-9\text{ m}$

Rational velocity and maximum speed

Rational velocity and maximum speed

Solution:

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