The acceleration (a)-time (t) graph for a par | vedclass

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

Question

(A) From the given acceleration $(a)$-time $(t)$ graph,it is evident that the acceleration is positive and decreasing linearly with time.Let the accel

Vedclass · Accepted Answer

Vedclass · Answer

(A) From the given acceleration $(a)$-time $(t)$ graph,it is evident that the acceleration is positive and decreasing linearly with time.Let the acceleration be represented as $a = a_0 - kt$,where $a_0$ is the initial acceleration and $k$ is a positive constant.Since the particle starts from rest,the initial velocity $v(0) = 0$.We know that $a = \frac{dv}{dt}$,so $\frac{dv}{dt} = a_0 - kt$.Integrating both sides with respect to time $t$:$\int_{0}^{v} dv = \int_{0}^{t} (a_0 - kt) dt$$v = a_0 t - \frac{1}{2} kt^2$.This equation represents a downward-opening parabola starting from the origin $(0,0)$.As time $t$ increases,the slope of the velocity-time graph,which is the acceleration $a$,decreases. Therefore,the velocity-time graph should be a curve that starts with a positive slope and becomes flatter (slope decreases) as time approaches $T$. This corresponds to the graph shown in option $(A)$.

$t (s)$	$0$	$1$	$2$	$3$
$x (m)$	$-2$	$0$	$6$	$16$

The acceleration $(a)$-time $(t)$ graph for a particle moving along a straight line starting from rest is shown in the figure. Which of the following graphs is the best representation of the variation of its velocity $(v)$ with time $(t)$?

Similar Questions

The position of a particle moving along the $X-$axis at certain times is given below. Which of the following describes the motion correctly?
$t (s)$ $0$ $1$ $2$ $3$
$x (m)$ $-2$ $0$ $6$ $16$

The relation between the displacement $x$ (in metre) and the time $t$ (in second) of a particle is $t = 2x^2 + 3x$. If the displacement of the particle is $25 \ cm$ from the origin $(x = 0)$, then the acceleration of the particle is:

The motion of a particle along a straight line is described by the function $x = (2t - 3)^2$,where $x$ is in metres and $t$ is in seconds. The acceleration of the particle at $t = 2 \,s$ is (in $\,m/s^2$)

What can be the angle between velocity and acceleration for the motion on a straight line? Explain with an example.

Let $\vec v$ and $\vec a$ denote the velocity and acceleration respectively of a body in one-dimensional motion. Which of the following statements is correct regarding the speed of the body?

Vedclass Test Series

Exam Paper Generator

Online Exam Module