A particle passes through $O$ at time $t=0$ with velocity $1\text{ m s}^{-1}$. Its acceleratio

Question

A particle passes through $O$ at time $t=0$ with velocity $1\text{ m s}^{-1}$. Its acceleration is $a=\dfrac{6}{(t+1)^2}\text{ m s}^{-2}$, where $t\geq0$. (i) Find the velocity of the particle in terms of $t$. (ii) Hence find its displacement from $O$ in terms of $t$. (iii) Find the distance travelled in the first $3$ seconds.

Accepted Answer

(i) $v=7-\dfrac6{t+1}\text{ m s}^{-1}$ (ii) $s=7t-6\ln(t+1)\text{ m}$ (iii) $21-6\ln4\text{ m}$

Inverse-square acceleration

Inverse-square acceleration

Solution:

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