A particle of mass m moves on the x-axis as f | vedclass

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

Question

(D) The particle starts from rest at $x = 0$ ($v = 0$ at $t = 0$) and comes to rest at $x = 1$ ($v = 0$ at $t = 1$).Since the particle moves from $x =

Vedclass · Accepted Answer

Both $(a)$ and $(c)$

Vedclass · Answer

(D) The particle starts from rest at $x = 0$ ($v = 0$ at $t = 0$) and comes to rest at $x = 1$ ($v = 0$ at $t = 1$).Since the particle moves from $x = 0$ to $x = 1$,its average velocity is positive. For the particle to start from rest and end at rest,it must accelerate initially to gain velocity and decelerate later to come to a stop.If $\alpha$ remained positive for the entire interval $0 \le t \le 1$,the velocity would be strictly increasing,meaning the particle could not return to rest at $t = 1$.Therefore,$\alpha$ cannot remain positive for all $t$ in the interval $0 \le t \le 1$,which implies $\alpha$ must change sign during the motion.Thus,both statements $(a)$ and $(c)$ are correct.

Similar Questions

At time $t=0$, a particle leaves the origin and moves in the positive direction of the $X$-axis. If the velocity of the particle varies as $v(t)=v_0(1-t/t_0)$, where $|v_0|=10 \ m/s$ and $t_0=10 \ s$, then the distance covered by the particle during the first $20 \ s$ is: (in $m$)

Which of the following four statements is false?

If a car covers $2/5^{th}$ of the total distance with speed $v_1$ and $3/5^{th}$ of the total distance with speed $v_2$,then the average speed is:

$A$ car starts from rest and moves with a constant acceleration of $5 \,m/s^2$ for $10 \,s$ before the driver applies the brake. It then decelerates for $5 \,s$ before coming to rest. The average speed of the car over the entire journey is: (in $\,m/s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module