Acceleration of particle moving rectilinearly is a = 4 - 2 x (where x is the position in meter and a in m s - 2 ). It is at instantaneous rest at x = 0 . At what position x (in meter ) will the particle again come to instantaneous rest?

Given Acceleration is, a = 4 - 2 x We know that rate of change of displacement is called velocity and rate of change of velocity is called acceleration so, a = v d v d x = 4 - 2 x Also, at t = 0 , x = 0 and v = 0 Let integrate the given equation, ⇒ ∫ 0 v v d v = ∫ 0 x 4 - 2 x d x ⇒ v 2 2 = 4 x - x 2 when v = 0 , 4 x - x 2 = 0 x = 0 , 4 Thus, at x = 4 , the particle will again come to rest.

A particle is projected vertically from the ground takes time t 1 = 1 s up to point A , t 2 = 3 s from point A to B , and time t 3 = 4 s from point B to the highest point. Find the height of the middle point of A and B from the ground.

Time taken by the particle to reach the highest point t = t 1 + t 2 + t 3 = 8 s . Now applying the first equation of motion, At the highest point, v = u + a t ⇒ 0 = u - 10 × 8 ⇒ u = 80 m s - 1 . Height of point A h A = u t + 1 2 a t 2 ⇒ h A = 10 × 1 - 1 2 10 × 1 2 = 75 m . Height of point B h B = u t + 1 2 a t 2 ⇒ h B = 10 × 4 - 1 2 10 × 4 2 = 240 m . Height of A B h AB = h B - h A = 240 - 75 = 165 m . So, the height of the middle point of A B h middle = h A + h AB 2 = 75 + 165 2 = 157 . 5 m .

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A particle can move only along $x -$ axis. Three pairs of initial and final positions of particle at two successive times are given

Pair Initial position Final position

$1$ $- 3 m$ $+ 5 m$

$2$ $- 3 m$ $- 7 m$

$3$ $+ 7 m$ $- 3 m$

Find the sum of magnitudes of displacement in the pairs which give negative displacement in $m$ .

Important Questions on Kinematics I

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 14

The figure shows a method for measuring the acceleration due to gravity. The ball is projected upward by a gun. The ball passes electronic "gates" $1$ and $2$ as it rises and again as it falls. Each gate is connected to a separate timer. The first passage of the ball through each gate starts the corresponding timer, and the second passage through the same gate stops the timer. The time intervals $△ t_{1}$ and $△ t_{2}$ are thus measured. The vertical distance between the two gates is $d$ . If $d = 5 m$ , $△ t_{1} = 3 s$ , $△ t_{2} = 2 s$ , find the measured value of acceleration due to gravity . (in ${ms}^{- 2}$ ).

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 15

Acceleration of particle moving rectilinearly is

a = 4 - 2 x

(where

x

is the position in

meter

and

a

m s^{- 2}

). It is at instantaneous rest at

x = 0

. At what position

x

(in

meter

) will the particle again come to instantaneous rest?

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 16

A big Diwali rocket is projected vertically upward to attain a maximum height of

160 m

. The rocket explodes just as it reaches the top of its trajectory sending out luminous particles in all possible directions all with the same speed

v

. The display, consisting of the luminous particles, spreads out as an expanding, brilliant sphere. The bottom of this sphere just touches the ground when its radius is

80 m

. With what (in

m s^{- 1}

) are the luminous particle ejected by the explosion?

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 17

A steel ball is dropped from the roof of a building. A man standing in front of a

1 m

high window in the building notes that the ball takes

0.1 s

to the fall from the top to the bottom of the window. The ball continues to fall and strikes the ground. On striking the ground, the ball gets rebounded with the same speed with which it hits the ground. If the ball reappears at the bottom of the window

2 s

after passing the bottom of the window on the way down, find the height of the building.

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 18

A passenger reaches the platform and finds that the second last boggy of the train is passing him. The second last boggy takes

3 s

to pass the passenger, and the last boggy takes

2 s

to pass him. Find the time by which the passenger late for the departure of the train? Assume that the train accelerates at a constant rate and all the boogies are of equal length.

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 19

A particle is projected vertically from the ground takes time

t_{1} = 1 s

up to point

A

t_{2} = 3 s

from point

A

B

, and time

t_{3} = 4 s

from point

B

to the highest point. Find the height of the middle point of

A

and

B

from the ground.

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 20

The loaded bucket of a crane achieves a maximum velocity

5 m s^{- 1}

in some time at a uniform rate and then takes half of this time to stop at a uniform rate after the application of the brake. The time difference between the instants when half of the maximum velocity is achieved is

t (\sec)

. Find the displacement of the bucket.

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 4 - Kinematics I>Exercises>Q 21

The velocity-time graph for the vertical component of the velocity of an object thrown upward from the ground which reaches the roof of a building is shown in the figure. If the height of the building is $h meter$ . Find $\frac{h}{5}$ .

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Pair	Initial position	Final position
$1$	$- 3 m$	$+ 5 m$
$2$	$- 3 m$	$- 7 m$
$3$	$+ 7 m$	$- 3 m$

A particle can move only along x-axis. Three pairs of initial and final positions of particle at two successive times are given Pair Initial position Final position 1 -3 m +5 m 2 -3 m -7 m 3 +7 m -3 m Find the sum of magnitudes of displacement in the pairs which give negative displacement in m.

Important Questions on Kinematics I

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