Question

$x=3+8t-4t^2$ is the distance traveled by a particle in $\mathrm{t}$ seconds. Its velocity will be after 1 second

• A. $0\mathrm{unit}$
• B. $3\mathrm{units}$
• C. $4\mathrm{units}$
• D. $7\mathrm{units}$

Answer 1

The correct option is A

$0\mathrm{unit}$

Step:1 Given data:

The distance covered by the particle is $x=3+8t-4t^2····\left(1\right)$

Step: 2 Formula used:

The relation between displacement and velocity is

$v=\frac{\mathrm{dx}}{\mathrm{dt}}$

Step: 3 Compute the velocity

Differentiate equation $\left(1\right)$ to obtain the velocity.

$$\begin{gathered} \frac{dx}{dt}=8-8t \\ v=8-8t \end{gathered}$$

The velocity after one second is

$\begin{array}{rcl}{v}_{t=1}& =& 8-8\left(1\right)\\ & =& 0\end{array}$

Hence option A is the correct answer.