Question

The distance travelled by a particle is related to time $t$ as $x=4 t^2$ The velocity of the particle at $t-5 s$ is:-

• A. $8 \,m s^{-1}$
• B. $20\, ms ^{-1}$
• C. $25\, ms ^{-1}$
• D. $40\, ms ^{-1}$

Answer 1

The Correct Option is D

The correct answer is (D) : $40\, ms ^{-1}$
$x=4t^2$
$v=\frac{dx}{dt}=8t$
At $t=5sec$
$v=8\times 5=40m/s$

Answer 2

The velocity \( v \) of the particle is the derivative of the position with respect to time. Given the position function: \[ v = \frac{dx}{dt} = \frac{d}{dt}(4t^2) = 8t \] At \( t = 5 \) seconds, the velocity is: \[ v = 8 \times 5 = 40 \, \text{m/s} \]