A particle of mass $m$ moves on the x-axis as follows : it starts from rest at $t = 0$ from the point $x = 0$ and comes to rest at $ t= 1$ at the point $x = 1$. No other information is available about its motion at intermediate time $(0 < t < 1)$. If $\alpha $ denotes the instantaneous acceleration of the particle, then
A particle of mass $m$ moves on the x-axis as follows : it starts from rest at $t = 0$ from the point $x = 0$ and comes to rest at $ t= 1$ at the point $x = 1$. No other information is available about its motion at intermediate time $(0 < t < 1)$. If $\alpha $ denotes the instantaneous acceleration of the particle, then
- [IIT 1993]
- A
$\alpha $ cannot remain positive for all $t$ in the interval $0 \le t \le 1$
- B
$|\alpha |$ cannot exceed 2 at any point in its path
- C
$\alpha $ must change sign during the motion but no other assertion can be made with the information given
- D
(a) and (c) both
Similar Questions
In the $s-t$ equation $\left(s=10+20 t-5 t^2\right)$, match the following columns.
Colum $I$
Colum $II$
$(A)$ Distance travelled in $3\,s$
$(p)$ $-20$ units
$(B)$ Displacement in $1\,s$
$(q)$ $15$ units
$(C)$ Initial acceleration
$(r)$ $25$ units
$(D)$ Velocity at $4\,s$
$(s)$ $-10$ units
| Colum $I$ | Colum $II$ |
| $(A)$ Distance travelled in $3\,s$ | $(p)$ $-20$ units |
| $(B)$ Displacement in $1\,s$ | $(q)$ $15$ units |
| $(C)$ Initial acceleration | $(r)$ $25$ units |
| $(D)$ Velocity at $4\,s$ | $(s)$ $-10$ units |
If the velocity-time graph has the shape $AMB$, what would be the shape of the corresponding acceleration-time graph ?
If the velocity-time graph has the shape $AMB$, what would be the shape of the corresponding acceleration-time graph ?
- [JEE MAIN 2021]
A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time (Take acceleration in the backward direction as positive).
A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time (Take acceleration in the backward direction as positive).
The displacement versus time graph for a body moving in a straight line is shown in figure. Which of the following regions represents the motion when no force is acting on the body
Position time graph of a particle moving along straight line is shown which is in the form of semicircle starting from $t=2$ to $t=8 \,s$. Select correct statement
Position time graph of a particle moving along straight line is shown which is in the form of semicircle starting from $t=2$ to $t=8 \,s$. Select correct statement