Question

The distance moved by a particle travelling in a straight line in t seconds is given by $s=45t+11t^2-t^3$. the time taken by the particle to come to rest is .

• A. 9 seconds
• B. 5/3 seconds
• C. 3/5 seconds
• D. 2 seconds

Answer 1

The correct option is A 9 seconds

The distance moves by the particle travelling in a straight line in t seconds is given by $s=45t+11t^2-t^3$The speed of the particle at any instant t is given by
$\frac{\mathrm{ds}}{\mathrm{dt}}.$When the particle comes to rest $\frac{\mathrm{ds}}{\mathrm{dt}}=0\mathrm{Differentiating}\left(1\right]w.r.t.t,\mathrm{we}\mathrm{get}\frac{\mathrm{ds}}{\mathrm{dt}}=45+22t-3t^2\mathrm{Now},\frac{\mathrm{ds}}{\mathrm{dt}}=0\Rightarrow 45+22t-3t^2=0\Rightarrow 3t^2-22t-45=0\Rightarrow \left(t-9\right)\left(3t+5\right)=0\Rightarrow t=9\mathrm{or}-\frac{5}{3}\left(\mathrm{which}\mathrm{is}\mathrm{not}\mathrm{possible}\right)$
Therefore, particle comes to rest after 9 seconds.