Question

The distance traveled $s$ (in metres) by a particle in $t$ seconds is given by $s=t^3+2t^2+1$. The speed of the particle after $1second$ will be

• A. $8cm/sec$
• B. $6cm/sec`$
• C. $2cm/sec$
• D. None of these

Answer 1

The correct option is D

None of these

Step 1: Given data

Distance traveled by particle=$s$

Time is taken to travel a distance=$t$

Relation between $s$ and $t$, $s=t^3+2t^2+1$

Step 2: Formula used

We know that the $\frac{ds}{dt}$ will give us the expression for the speed $v$ of the particle at any time $t$. So,

$v=\frac{ds}{dt}$

Step 3: Speed of particle at a time $t$

Using the formula to differentiate distance with respect to time-

$\begin{array}{rcl}s& =& t^3+2t^2+t\\ \frac{ds}{dt}& =& 3t^2+4t+1\\ {\left(\frac{ds}{dt}\right)}_{t=1}& =& 3\times 1^2+4\times 1+1\\ {\left(\frac{ds}{dt}\right)}_{t=1}& =& 8m/sec\end{array}$

Thus, the speed of the particle after $1second$ will be $8m/sec$.

Hence, option D is the correct answer.