(C) When the video is played in reverse,the time variable $t$ is replaced by $-t$. $1$. Position vector $\vec{r}(t)$ remains the same at the specific

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(C) When the video is played in reverse,the time variable $t$ is replaced by $-t$. $1$. Position vector $\vec{r}(t)$ remains the same at the specific moment $A$ because the object is at the same spatial location,so $\vec{r}_{obs} = \vec{r}$. $2$. Velocity is defined as $\vec{v} = \frac{d\vec{r}}{dt}$. In reverse,$\vec{v}_{obs} = \frac{d\vec{r}}{d(-t)} = -\frac{d\vec{r}}{dt} = -\vec{v}$. $3$. Acceleration is defined as $\vec{a} = \frac{d\vec{v}}{dt}$. In reverse,$\vec{a}_{obs} = \frac{d(\vec{v}_{obs})}{d(-t)} = \frac{d(-\vec{v})}{-dt} = \frac{d\vec{v}}{dt} = \vec{a}$. Thus,the observed values are $\vec{r}, -\vec{v}, \vec{a}$.

Class 11 Physics Motion in Straight Line Mix Examples-Motion in Straight Line

Difficult

$A$ charged object is launched inside a time-varying electric field. Its motion is recorded by a video camera on a video tape. When it is at a certain moment $A$,its position vector $\vec{r}$,velocity $\vec{v}$,and acceleration $\vec{a}$ are measured. $A$ student watches the video at a later time but mistakenly plays the tape in the reverse direction. What are the position,velocity,and acceleration of the object at moment $A$ observed by the student,respectively?

A
$\vec{r}, \vec{v}, \vec{a}$
B
$-\vec{r}, -\vec{v}, -\vec{a}$
C
$\vec{r}, -\vec{v}, \vec{a}$
D
$\vec{r}, \vec{v}, -\vec{a}$

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Motion in Straight Line

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Mix Examples-Motion in Straight Line

At time $t=0$,a car moving along a straight line has a velocity of $16 \; m/s$. It slows down with an acceleration of $a = -0.5t \; m/s^2$,where $t$ is in seconds. Mark the correct statement$(s)$.

Difficult

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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 $m$)

DifficultTS EAMCET 2021

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$A$ body of mass $0.40 \;kg$ moving initially with a constant speed of $10 \;m s^{-1}$ to the north is subject to a constant force of $8.0 \;N$ directed towards the south for $30 \;s$. Take the instant the force is applied to be $t=0$,the position of the body at that time to be $x=0$,and predict its position at $t=-5 \;s, 25 \;s, 100 \;s$.

Medium

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Two stones are thrown up simultaneously from the edge of a cliff $240 \ m$ high with initial speeds of $10 \ m/s$ and $40 \ m/s$ respectively. Which of the following graphs best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance,take $g = 10 \ m/s^2$)

MediumJEE MAIN 2015

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$A$ particle moving in a straight line covers half the distance with speed $6 \, m/s$. The other half is covered in two equal time intervals with speeds $9 \, m/s$ and $15 \, m/s$ respectively. The average speed of the particle during the motion is: (in $ \, m/s$)

DifficultJEE MAIN 2024

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At time $t=0$,a car moving along a straight line has a velocity of $16 \; m/s$. It slows down with an acceleration of $a = -0.5t \; m/s^2$,where $t$ is in seconds. Mark the correct statement$(s)$.

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 $m$)

$A$ particle moving in a straight line covers half the distance with speed $6 \, m/s$. The other half is covered in two equal time intervals with speeds $9 \, m/s$ and $15 \, m/s$ respectively. The average speed of the particle during the motion is: (in $ \, m/s$)

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