(B) At maximum height,the final velocity $v = 0$.Using the first equation of motion,$v = u + at$:$0 = u - gT \Rightarrow u = gT$.To find the time $t$

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It acquires velocity $u/2$ in $T/2 \ s$.

(B) At maximum height,the final velocity $v = 0$.Using the first equation of motion,$v = u + at$:$0 = u - gT \Rightarrow u = gT$.To find the time $t$ when the velocity is $u/2$:$v = u - gt$$\frac{u}{2} = u - gt$$gt = \frac{u}{2}$Substituting $u = gT$ into the equation:$gt = \frac{gT}{2} \Rightarrow t = \frac{T}{2}$.Thus,the body acquires a velocity of $u/2$ at time $t = T/2$.

Class 11 Physics Motion in Straight Line Motion Under Gravity

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$A$ body is projected upwards with a speed $u$ and the time taken by it to reach the maximum height $H$ is $T$. Pick out the correct statement.

A
It reaches $H/2$ in $T/2 \ s$.
B
It acquires velocity $u/2$ in $T/2 \ s$.
C
Its velocity is $u/2$ at $H/2$.
D
It has the same velocity at $2T$.

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Motion in Straight Line

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Motion Under Gravity

$A$ ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).
$(a)$ Plot qualitatively velocity versus time graph.
$(b)$ Plot qualitatively acceleration versus time graph.

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$A$ stone is dropped into water from a bridge $44.1 \ m$ above the water. Another stone is thrown vertically downward $1 \ s$ later. Both strike the water simultaneously. What was the initial speed of the second stone in $m/s$?

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$A$ stone dropped from the top of a tower of height $300 \; m$ splashes into the water of a pond near the base of the tower. When is the splash heard at the top,given that the speed of sound in air is $340 \; m s^{-1}$ (in $; s$)? $(g = 9.8 \; m s^{-2})$

Medium

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$A$ body,thrown upwards with some velocity,reaches a maximum height of $50 \,m$. Another body with double the mass,thrown up with double the initial velocity,will reach a maximum height of............$m$.

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$A$ stone is thrown vertically up from the top end of a window of height $1.8 \,m$ with a velocity of $8 \,m/s$. The time taken by the stone to cross the window during its downward journey is (Acceleration due to gravity $= 10 \,m/s^2$) (in $\,s$)

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$A$ body is projected upwards with a speed $u$ and the time taken by it to reach the maximum height $H$ is $T$. Pick out the correct statement.

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$A$ ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).$(a)$ Plot qualitatively velocity versus time graph.$(b)$ Plot qualitatively acceleration versus time graph.

$A$ stone is dropped into water from a bridge $44.1 \ m$ above the water. Another stone is thrown vertically downward $1 \ s$ later. Both strike the water simultaneously. What was the initial speed of the second stone in $m/s$?

$A$ stone dropped from the top of a tower of height $300 \; m$ splashes into the water of a pond near the base of the tower. When is the splash heard at the top,given that the speed of sound in air is $340 \; m s^{-1}$ (in $; s$)? $(g = 9.8 \; m s^{-2})$

$A$ body,thrown upwards with some velocity,reaches a maximum height of $50 \,m$. Another body with double the mass,thrown up with double the initial velocity,will reach a maximum height of............$m$.

$A$ stone is thrown vertically up from the top end of a window of height $1.8 \,m$ with a velocity of $8 \,m/s$. The time taken by the stone to cross the window during its downward journey is (Acceleration due to gravity $= 10 \,m/s^2$) (in $\,s$)

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$A$ ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).
$(a)$ Plot qualitatively velocity versus time graph.
$(b)$ Plot qualitatively acceleration versus time graph.