A particle starts from rest and undergoes an | vedclass

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

Question

(A) The acceleration-time $(a-t)$ graph shows that for $0 \le t \le 10 	ext{ s}$,acceleration $a$ increases linearly with time $t$. The equation for

Vedclass · Accepted Answer

Vedclass · Answer

(A) The acceleration-time $(a-t)$ graph shows that for $0 \le t \le 10 	ext{ s}$,acceleration $a$ increases linearly with time $t$. The equation for this line is $a = kt$. At $t = 10 	ext{ s}$,$a = 2 	ext{ m/s}^2$,so $2 = k(10)$,which gives $k = 0.2 	ext{ s}^{-2}$. Thus,$a = 0.2t$. Since $a = dv/dt$,we have $dv = a \, dt = 0.2t \, dt$. Integrating from $t = 0$ to $t = 10 	ext{ s}$ with $v(0) = 0$,we get $v = \int_0^t 0.2t \, dt = 0.1t^2$. This is a parabolic curve (concave upwards). At $t = 10 	ext{ s}$,$v = 0.1(10)^2 = 10 	ext{ m/s}$.For $10 \le t \le 15 	ext{ s}$,the acceleration is constant at $a = 1 	ext{ m/s}^2$. Since $a = dv/dt$ is constant,the velocity-time graph will be a straight line with a positive slope of $1 	ext{ m/s}^2$. The velocity at $t = 15 	ext{ s}$ will be $v = 10 + 1(15 - 10) = 15 	ext{ m/s}$. Thus,the graph is a parabola for the first part and a straight line for the second part.

$A$ particle starts from rest and undergoes an acceleration as shown in the figure. The velocity-time graph from the figure will have which shape?

Similar Questions

What is the maximum acceleration of the train during the journey in $km \ h^{-2}$?

The following plots show the variation of velocity $(v)$ with time $(t)$ for a ball thrown vertically upward and falling back. Which of the following plots is correct?

The figure shows a velocity-time graph of a particle moving along a straight line. The particle comes to rest at $t = \dots \text{sec}$.

$A$ train moves from one station to another in $2$ hours. Its speed-time graph during this motion is shown in the figure. The maximum acceleration during the journey is ............. $km\, h^{-2}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module