In the $s-t$ equation $(s=10+20t-5t^2)$,match the following columns.
Column $I$ Column $II$ $(A)$ 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
| Column $I$ | Column $II$ |
| $(A)$ 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 |
- A$(A \rightarrow r, B \rightarrow q, C \rightarrow s, D \rightarrow p)$
- B$(A \rightarrow p, B \rightarrow p, C \rightarrow s, D \rightarrow r)$
- C$(A \rightarrow r, B \rightarrow s, C \rightarrow p, D \rightarrow p)$
- D$(A \rightarrow s, B \rightarrow p, C \rightarrow r, D \rightarrow p)$
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Similar Questions
Select the incorrect statement among the following$:-$
$S_1 :$ If the acceleration is zero,a moving particle will perform uniform motion.
$S_2 :$ Motion with constant speed may or may not be uniform motion.
$S_3 :$ If a particle moves on a curved path,its acceleration can never be zero.
$S_4 :$ In successive time intervals,if the average velocities of a particle are equal,then the particle must be moving with uniform velocity.
$S_1 :$ If the acceleration is zero,a moving particle will perform uniform motion.
$S_2 :$ Motion with constant speed may or may not be uniform motion.
$S_3 :$ If a particle moves on a curved path,its acceleration can never be zero.
$S_4 :$ In successive time intervals,if the average velocities of a particle are equal,then the particle must be moving with uniform velocity.
Medium
View SolutionIn what different ways can the velocity of an object be changed?
Medium
View SolutionStatement $(I)$: An object subjected to velocities $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ has a resultant velocity with magnitude $|\vec{v}| = |\overrightarrow{v_1}| + |\overrightarrow{v_2}|$.
Statement $(II)$: The magnitude of displacement is either less than or equal to the path length of an object between two points.
Statement $(III)$: The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero.
Which of the following is correct?
Statement $(II)$: The magnitude of displacement is either less than or equal to the path length of an object between two points.
Statement $(III)$: The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero.
Which of the following is correct?
$A$ ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2$. Neglecting subsequent motion and air resistance,its velocity $v$ varies with the height $h$ above the ground as:
DifficultIIT 2000
View Solution$A$ particle starts moving from time $t=0$ and its coordinate is given as $x(t)=4t^{3}-3t.$ Which of the following statements are correct?
$A$. The particle returns to its original position (origin) at $t = \frac{\sqrt{3}}{2} \approx 0.866$ units later.
$B$. The particle is $1$ unit away from the origin at its turning point.
$C$. Acceleration of the particle is non-negative for $t \ge 0$.
$D$. The particle is $0.5$ units away from the origin at its turning point.
$E$. The particle never turns back as acceleration is non-negative.
$A$. The particle returns to its original position (origin) at $t = \frac{\sqrt{3}}{2} \approx 0.866$ units later.
$B$. The particle is $1$ unit away from the origin at its turning point.
$C$. Acceleration of the particle is non-negative for $t \ge 0$.
$D$. The particle is $0.5$ units away from the origin at its turning point.
$E$. The particle never turns back as acceleration is non-negative.
DifficultJEE MAIN 2026
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