The velocity (v)-time (t) graph for a particl | vedclass

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

Question

(A) The velocity $(v)$ is the slope of the position $(x)$-time $(t)$ graph,i.e.,$v = \frac{dx}{dt}$.In the first interval,the velocity increases linea

Vedclass · Accepted Answer

Vedclass · Answer

(A) The velocity $(v)$ is the slope of the position $(x)$-time $(t)$ graph,i.e.,$v = \frac{dx}{dt}$.In the first interval,the velocity increases linearly from $0$ to a maximum value. Since $v = at$ (where $a$ is constant acceleration),the position $x = \int v dt = \frac{1}{2}at^2$,which is a parabola opening upwards.In the second interval,the velocity is negative and its magnitude decreases linearly to $0$. This implies a negative acceleration (deceleration). The position $x$ will follow a parabolic path that returns to the initial position (or a specific point) with a decreasing slope.The correct graph shows a parabolic increase in position followed by a parabolic decrease,which matches the shape where the slope of the $x-t$ graph corresponds to the given $v-t$ graph.

The velocity $(v)$-time $(t)$ graph for a particle moving along the $x$-axis is shown in the figure. The corresponding position $(x)$-time $(t)$ graph is best represented by:

Similar Questions

What is the acceleration of the particle on $OA$,$AB$,and $BC$ respectively?

For a body moving along a straight line, the following $v-t$ graph is obtained. According to the graph, the displacement during

The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\,[1 - {e^{ - bt}}]$. Then the velocity of the particle is

Which of the following speed-time $(v-t)$ graphs is physically not possible?

The area under an acceleration-time graph gives:

Vedclass Test Series

Exam Paper Generator

Online Exam Module