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A particle moving with a uniform acceleration travels $24 m$ and $64 m$ in the first two consecutive intervals of $4 s$ each. Its initial velocity will be

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Important Questions on Dynamics

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Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

In a car race, two cars start with velocities

u_{1}

and

u_{2}

and travel along a straight line with accelerations

α

and

β

respectively. If both reach the finish line at the same time then range of the race is

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

An object is thrown vertically with a velocity

u

. The velocity with which it strikes the ground on its return is

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A ball is projected vertically up from ground. Boy

' A'

standing at the window of first floor of a nearby building observes that the time interval between the ball crossing him while going up and the ball crossing him while going down is

2 s

. Another boy

B

standing on the second floor notices the time interval between the ball passing him twice, during up and down motion is

1 s

. Calculate the difference between the vertical positions of boy

B

and boy

A

. (Assume

g = 10 m s^{- 2}

)

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

Two particles

A

and

B

move from rest along a straight line with constant accelerations

f

and

h,

respectively. If

A

takes

m

seconds more than

B

and describes

n

units more than that of

B

acquiring the same speed, then

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A stone thrown down with a seed

u

takes a time

t_{1}

to reach the ground, while another stone, thrown upwards from the same point with the same speed, takes time

t_{2}

. The maximum height the second stone reaches from the ground is

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A particle is projected vertically upwards. If it has to stay above the ground for

12 \sec

, then

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A helicopter rises from rest on the ground vertically upwards with a constant acceleration

g

. A food packet is dropped from the helicopter when it is at a height

h

. The time taken by the packet to reach the ground is close to [

g

is the acceleration due to gravity]:

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A ball is dropped from the top of the building

100 m

high. Simultaneously, another ball is thrown upwards from the bottom of the building with such a velocity that the balls collide exactly mid-way. What is the speed in

m s^{- 1}

with which the second ball is thrown? (Take

g = 10 m s^{- 2}

)

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x - a x i s$ . Identify all figures that correctly represent the motion qualitatively.
( $a =$ acceleration, $v =$ velocity, $x =$ dispalcement, $t =$ time)
$(A)$ Question Image
$(B)$
$(C)$
$(D)$

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

An object with mass

5 kg

is acted upon by a force,

\vec{F} = (- 3 \hat{i} + 4 \hat{j}) N

. If its initial velocity at

t = 0

\vec{v} = (6 \hat{i} - 12 \hat{j}) {ms}^{- 1},

the time at which it will just have a velocity along y-axis is

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A particle has initial velocity

(2 \hat{i} + 3 \hat{j})

and acceleration

(0.3 \hat{i} + 0.2 \hat{j})

. The magnitude of velocity after

10

seconds will be

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

In a car race on straight road, car

A

takes a time

t

less than car

B

at the finish and passes finishing point with a speed

v

more than that of car

B .

Both the cars start from rest and travel with constant acceleration

a_{1}

and

a_{2}

respectively. Then $v$ is equal to:

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A ball is dropped from a height of

19.6 m

. The distance covered by it in the last second is

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

From the top of a tower of height

H

, a body is thrown vertically upwards with a speed

u

. Time taken by the body to reach the ground is

3

times the time taken by it to reach the highest point in its path. Then, the speed

u

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A body moving with uniform acceleration

6 m / s^{2}

starts from rest. The distance covered by it in

4^{th}

second will be

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A boy pushes a box of mass

2 kg

with a force

\vec{F} = (20 \hat{i} + 10 \hat{j}) N

on a frictionless surface. If the box was initially at rest, then _______

m

is displacement along the

x

-axis after

10 s

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity

u

and the last compartment with velocity

v

. The velocity with which middle point of the train passes the signal post is :

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A ship of mass

2 \times 10^{7} kg

initially at rest is pulled by a force of

5 \times 10^{5} N

, through a distance of

2 m

. Assuming that the resistance due to water is negligible, the speed of the ship is

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A parachutist with total weight

75 kg

drops vertically onto a sandy ground with a speed of

2 m s^{- 1}

and comes to a halt over a distance of

0.25 m

. The average force from the ground on her is close to-

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A piece of wood of mass

0.03 kg

is dropped from the top of a

100 m

height building. At the same time, a bullet of mass

0.02 kg

is fired vertically upward, with a velocity

100 m s^{- 1},

from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is:

(g = 10 m s^{- 2})

A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 s each. Its initial velocity will be

Important Questions on Dynamics

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A particle moving with a uniform acceleration travels $24 m$ and $64 m$ in the first two consecutive intervals of $4 s$ each. Its initial velocity will be