The distance travelled by a particle is direc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that the distance $s$ is proportional to $t^{1/2}$,we can write $s = k t^{1/2}$,where $k$ is a constant.The velocity $v$ is the first deriva

Vedclass · Accepted Answer

Decreasing retardation

Vedclass · Answer

(D) Given that the distance $s$ is proportional to $t^{1/2}$,we can write $s = k t^{1/2}$,where $k$ is a constant.The velocity $v$ is the first derivative of displacement with respect to time: $v = \frac{ds}{dt} = \frac{d}{dt}(k t^{1/2}) = \frac{1}{2} k t^{-1/2}$.The acceleration $a$ is the second derivative of displacement with respect to time: $a = \frac{dv}{dt} = \frac{d}{dt}(\frac{1}{2} k t^{-1/2}) = -\frac{1}{4} k t^{-3/2}$.The negative sign indicates that the acceleration is in the opposite direction of motion,which represents retardation (deceleration).As time $t$ increases,the magnitude of acceleration $|a| = \frac{k}{4 t^{3/2}}$ decreases.Therefore,the motion is characterized by decreasing retardation.

The distance travelled by a particle is directly proportional to $t^{1/2}$,where $t =$ time elapsed. What is the nature of motion?

Similar Questions

$A$ rifle bullet loses $1/20^{th}$ of its velocity in passing through a wooden plank. The least number of planks required to stop the bullet is :-

$A$ car is moving with a speed of $150 \ km/h$ and after applying the brakes,it travels $27 \ m$ before it stops. If the same car is moving with a speed of one-third of the initial speed,then it will stop after traveling how many meters?

Consider that a truck is moving initially with $54 \,km/h$. It is stopped by the driver after looking at an obstacle with a deceleration of $10 \,m/s^2$. The distance travelled by the truck before coming to rest is (in $\,m$)

If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module