The distance travelled by a body moving along | vedclass

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

Question

(B) Given that the distance (or displacement) $s$ is proportional to $t^3$,we can write:$s = k t^3$ (where $k$ is a constant).To find the velocity $v$

Vedclass · Accepted Answer

Vedclass · Answer

(B) Given that the distance (or displacement) $s$ is proportional to $t^3$,we can write:$s = k t^3$ (where $k$ is a constant).To find the velocity $v$,we differentiate $s$ with respect to time $t$:$v = \frac{ds}{dt} = \frac{d}{dt}(k t^3) = 3k t^2$.To find the acceleration $a$,we differentiate the velocity $v$ with respect to time $t$:$a = \frac{dv}{dt} = \frac{d}{dt}(3k t^2) = 6k t$.Since $a = 6k t$,it implies that $a \propto t$.This represents a linear relationship passing through the origin,which corresponds to a straight line graph starting from the origin.Looking at the provided options,the graph that shows $a$ increasing linearly with $t$ is Graph $B$.

The distance travelled by a body moving along a line in time $t$ is proportional to $t^3$. The acceleration-time $(a, t)$ graph for the motion of the body will be

Similar Questions

$A$ particle starts from rest. Its acceleration $(a)$ versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be (in $m \ s^{-1}$)

$A$ body starts from the origin and moves along the $x$-axis such that its position at any instant is $x = 4t^2 - 12t$,where $t$ is in seconds and $x$ is in meters. What is the acceleration of the particle in $m/s^2$?

$Assertion$ : Retardation is directly opposite to the velocity.
$Reason$ : Retardation is equal to the time rate of decrease of speed.

If $v$ is the velocity of a body moving along the $x$-axis,then the acceleration of the body is .........

If the velocity of a particle is $(10 + 2t^2) \ m/s$,then the average acceleration of the particle between $2 \ s$ and $5 \ s$ is..........$m/s^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module