A particle is projected from ground in vertical upward direction at t = 0 , with initial velocity 48

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2.Motion in Straight Line

normal

A particle is projected from ground in vertical upward direction at $t = 0$, with initial velocity $48\, m/s$ and the distance travelled by particle in $5^{th}$ second is......$m$ $(g = 10\, m/s^2)$

$3$

$115$

$3.4$

$2.8$

Solution

$5^{\text {th }}$ sec $\Rightarrow t=4 \rightarrow t=5$

$\mathrm{S}_{4 \rightarrow 8}=$ Displacement in last $0.8\, sec$ of upward journey

$\mathrm{S}=\mathrm{vt}-\frac{1}{2} \mathrm{a}_{\mathrm{y}} \mathrm{t}^{2}, \mathrm{v}=0$

Assuming upward direction to be positive $(+i v e)$

$a_y=-g$

$S_{4 \rightarrow 4.8}=\frac{1}{2} \times g \times(0.8)^{2}=5 \times 0.64$

$\begin{aligned} \mathrm{S}_{4.8 \rightarrow 5}=& \mathrm{ut}+\frac{1}{2} \mathrm{at}^{2} \\ &=0+\frac{1}{2} \times 10 \times(0.2)^{2}=5 \times 0.04 \end{aligned}$

$\mathrm{S}_{4 \rightarrow 5}=5 \times 0.68=\frac{17}{5} \mathrm{m}$

Standard 11

Physics

Reaction time : When a situation demands our immediate action, it takes some time before we really respond. Reaction time is the time a person takes to observe, think and act. For example, if a person is driving and suddenly a boy appears on the road, then the time elapsed before he slams the brakes of the car is the reaction time. Reaction time depends on complexity of the situation and on an individual.

You can measure your reaction time by a simple experiment. Take a ruler and ask your friend to drop it vertically through the gap between your thumb and forefinger . After you catch it, find the distance $d$ travelled by the ruler. In a particular case, $d$ was found to be $21.0\; cm$. Estimate reaction time in second.

easy

A ball is dropped from a hetght of $90 \;m$ on a floor. At each colliston with the floor. the ball loses one tenth of its speed. Plot the speed-time graph of its motion between $t=0$ to $12 \;s$

medium

Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8\, {m}$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor. (In $m$)

hard

(JEE MAIN-2021)

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of……..$s$