The acceleration-time graph for a particle is | vedclass

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

Question

(A) The distance travelled is equal to the area under the velocity-time $(v-t)$ graph.First, we construct the $v-t$ graph from the given acceleration-

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) The distance travelled is equal to the area under the velocity-time $(v-t)$ graph.First, we construct the $v-t$ graph from the given acceleration-time $(a-t)$ graph:$1$. For $0 \le t \le 1 \, s$, $a = 2 \, m/s^2$. Since $v = \int a \, dt$, $v = 2t$. At $t = 1 \, s$, $v = 2 \, m/s$.$2$. For $1 \le t \le 2 \, s$, $a = 0$, so velocity remains constant at $v = 2 \, m/s$.$3$. For $2 \le t \le 3 \, s$, $a = -2 \, m/s^2$. Velocity decreases from $2 \, m/s$ to $0 \, m/s$ at $t = 3 \, s$.The resulting $v-t$ graph is a trapezoid with parallel sides of length $1 \, s$ (from $t=1$ to $t=2$) and $3 \, s$ (from $t=0$ to $t=3$), and height $2 \, m/s$.Distance = Area of the trapezoid = $\frac{1}{2} 	imes (	ext{sum of parallel sides}) 	imes 	ext{height}$Distance = $\frac{1}{2} 	imes (1 + 3) 	imes 2 = 4 \, m$.

The acceleration-time graph for a particle is given in the figure. If it starts motion at $t=0$, the distance travelled in $3 \, s$ will be ........... $m$.

Similar Questions

What will be the change in the speed of a moving object if both speed and acceleration are positive or both are negative?

The acceleration at the end of $2 \ s$ of a particle whose motion is represented by the equation $S = 4t^3 - 8t^2 + 5t + 4$ is $......$ (in $m \ s^{-2}$)

The velocity of a body depends on time according to the equation $v = 20 + 0.1t^2$. The body is undergoing

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 $(t)$?

The acceleration of a train between two stations is shown in the figure. The maximum speed of the train is $............\,m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module