A particle moves so that its position vector is given by r → = c o s ω t x ^ + s i n ω t y ^ , where ω is a constant. Which of the following is true?

Velocity is perpendicular to r → and acceleration is directed towards the origin.

Velocity and acceleration both are perpendicular to r → .

Velocity and acceleration both are parallel to r → .

Velocity is perpendicular to r → and acceleration is directed away from the origin.

HARD

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The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

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Important Questions on Kinematics

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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-

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

A particle is moving along with

X

-axis such that its acceleration is proportional to the displacement from the equilibrium position and they are in the same direction. The displacement

x (t)

is given by (where

ω > 0

is a constant)

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

A bullet loses

{(\frac{1}{n})}^{th}

of its velocity passing through one plank. Considering uniform retardation, the number of such planks that are required to stop the bullet can be:

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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:

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path.The relation between H, u and n is :

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

Two skaters, $P$ and $Q$ are skating towards each other. Skater, $P$ throws a ball towards, $Q$ every $5 s$ such that it always leaves her hand with speed $2 m s^{- 1}$ with respect to the ground. Consider two cases: (I) $P$ runs with speed $1 m s^{- 1}$ towards $Q,$ while $Q$ remains stationary. (II) $Q$ runs with speed $1 m s^{- 1}$ towards $P,$ while $P$ remains stationary. Note That irrespective of speed of $P,$ ball always leaves $P$ s hand with speed $2 m s^{- 1}$ with respect to the ground. Ignore gravity. Balls will be received by $Q .$

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

Average velocity of a particle executing SHM in one complete vibration is

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

A body moves along a straight line with acceleration

3 m s^{- 2}

for

2 s

and then with acceleration

4 m s^{- 2}

for

3 s.

What is his average acceleration?

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

Two cars

P

and

Q

start from a point at the same time in a straight line and their positions are represented by

X_{P} (t) = a t + b t^{2}

and

X_{Q} (t) = f t - t^{2}

. At what time do the cars have the same velocity?

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

A particle of mass

m

is acted upon by a force

F

given by the empirical law

F = \frac{R}{t^{2}} v (t) .

If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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})

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

Consider an expanding sphere of instantaneous radius

R

whose total mass remains constant. The expansion is such that the instantaneous density

ρ

remains uniform throughout the volume. The rate of fractional change in density

(\frac{1}{ρ} \frac{d ρ}{d t})

is constant. The velocity

v

of any point on the surface of the expanding sphere is proportional to

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

The

x

and

y

coordinates of the particle at any time are

x = 5 t - 2 t^{2}

and

y = 10 t

respectively, where

x

and

y

are in meters and

t

is in seconds. The acceleration of the particle at

t = 2 s

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

A ball is dropped from the top of a

100 m

high tower on a planet. In the last

\frac{1}{2} s

before hitting the ground, it covers a distance of

19 m .

Acceleration due to gravity (in

m s^{- 2}

) near the surface on that planet is______

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

The distance

x

covered by a particle in one dimensional motion varies with time

t

x^{2} = a t^{2} + 2 b t + c

. If the acceleration of the particle depends on

x

x^{- n}

, where

n

is an integer, the value of

n

is _________

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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
$(B)$
$(C)$
$(D)$

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity

(v)

vs time

(t)

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

In the cube of side $a$ shown in the figure, the vector from the central point of the face $A B O D$ to the central point of the face $B E F O$ will be:
Question Image

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

A particle moves so that its position vector is given by

\vec{r} = c o s ω t \hat{x} + s i n ω t \hat{y}

, where

ω

is a constant. Which of the following is true?

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

Important Questions on Kinematics

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