(A) For body $A$ starting from rest (initial velocity $u=0$): $S_A = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}at^2 = \frac{1}{2}at^2$ For body $B$ moving

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(A) For body $A$ starting from rest (initial velocity $u=0$): $S_A = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}at^2 = \frac{1}{2}at^2$ For body $B$ moving with uniform velocity $V$: $S_B = Vt$ Since they meet at the same point after time $t$,their displacements must be equal: $S_A = S_B$ $\frac{1}{2}at^2 = Vt$ Dividing both sides by $t$ (assuming $t \neq 0$): $\frac{1}{2}at = V$ $t = \frac{2V}{a}$

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

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Two bodies $A$ and $B$ start from the same point at the same instant and move along a straight line. Body $A$ moves with uniform acceleration $a$ and body $B$ moves with uniform velocity $V$. They meet after time $t$. The value of $t$ is

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A
$\frac{2V}{a}$
B
$\frac{a}{2V}$
C
$\frac{V}{2a}$
D
$\sqrt{\frac{V}{a}}$

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Class 11

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Motion in Straight Line

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Uniformly Accelerated Motion

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Give examples of a one-dimensional motion where:
$(a)$ The particle moving along positive $x$-direction comes to rest periodically and moves forward.
$(b)$ The particle moving along positive $x$-direction comes to rest periodically and moves backward.

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The velocity $v$ of a particle moving along the $x$-axis varies with its position $x$ as $v = \alpha \sqrt{x}$,where $\alpha$ is a constant. Which of the following graphs represents the variation of its acceleration $a$ with time $t$?

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The velocity of a bullet is reduced from $200\,m/s$ to $100\,m/s$ while travelling through a wooden block of thickness $10\,cm$. Assuming the retardation to be uniform,the retardation will be:

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$A$ particle initially at rest moves along the $x$-axis. Its acceleration varies with time as $a = 4t$. If it starts from the origin,the distance covered by it in $3 \ s$ is $........... \ m$.

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The average velocity of a body moving with uniform acceleration travelling a distance of $3.06 \ m$ is $0.34 \ ms^{-1}$. If the change in velocity of the body is $0.18 \ ms^{-1}$ during this time,its uniform acceleration is ......... $ms^{-2}$.

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Two bodies $A$ and $B$ start from the same point at the same instant and move along a straight line. Body $A$ moves with uniform acceleration $a$ and body $B$ moves with uniform velocity $V$. They meet after time $t$. The value of $t$ is

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Give examples of a one-dimensional motion where:$(a)$ The particle moving along positive $x$-direction comes to rest periodically and moves forward.$(b)$ The particle moving along positive $x$-direction comes to rest periodically and moves backward.

The velocity $v$ of a particle moving along the $x$-axis varies with its position $x$ as $v = \alpha \sqrt{x}$,where $\alpha$ is a constant. Which of the following graphs represents the variation of its acceleration $a$ with time $t$?

The velocity of a bullet is reduced from $200\,m/s$ to $100\,m/s$ while travelling through a wooden block of thickness $10\,cm$. Assuming the retardation to be uniform,the retardation will be:

$A$ particle initially at rest moves along the $x$-axis. Its acceleration varies with time as $a = 4t$. If it starts from the origin,the distance covered by it in $3 \ s$ is $........... \ m$.

The average velocity of a body moving with uniform acceleration travelling a distance of $3.06 \ m$ is $0.34 \ ms^{-1}$. If the change in velocity of the body is $0.18 \ ms^{-1}$ during this time,its uniform acceleration is ......... $ms^{-2}$.

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Give examples of a one-dimensional motion where:
$(a)$ The particle moving along positive $x$-direction comes to rest periodically and moves forward.
$(b)$ The particle moving along positive $x$-direction comes to rest periodically and moves backward.