The position vector of the particle is r t = a cos ⁡ ω t i ^ + a sin ⁡ ω t j ^ , where a and ω are real constants of suitable dimensions. The acceleration is

Perpendicular to the position vector

EASY

Earn 100

What is Dimensional Formula of Acceleration and its Derivation?

Important Questions on Motion in a Plane

MEDIUM

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A butterfly is flying with a velocity

4 \sqrt{2} m s^{- 1}

in north-east direction. Wind is slowly blowing at

1 m s^{- 1}

from north to south. The resultant displacement of the butterfly in

3

seconds is:

HARD

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

Three balls, $A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures, one kept on the ground and the other at height $h$ from the ground as shown in the figure. They take time $t_{A}$ and $t_{B}$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$ vertically above $X$ and reaches $X$ in time $t_{C}$ . Choose the correct statement.

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EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A swimmer can swim with velocity of $12 km / h$ in still water. Water flowing in a river has velocity $6 km / h$ . The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ________ $°$ .

(Round off to the Nearest Integer) (find the angle in degree)

MEDIUM

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A particle moves over a

x y

plane with a constant acceleration

\vec{a} = (4.0 m s^{- 2}) \hat{i} + (4.0 m s^{- 2} \hat{j})

. At the time

t = 0,

the velocity is

(4.0 m s^{- 2}) \hat{i} .

The speed of the particle when it is displaced by

6.0 m

parallel to the

x

-axis is,

MEDIUM

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A particle starts from the origin at

t = 0

with an initial velocity of

(3.0 \hat{i}) m s^{- 1}

and moves in the

x - y

plane with a constant acceleration

(6.0 \hat{i} + 4.0 \hat{j}) m s^{- 2}

. The

x -

coordinate of the particle at the instant when its

y -

coordinate is

32 m

D

meters. The value of

D

is:

HARD

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A particle starts from the origin at

t = 0 s

with a velocity of

10 \hat{j} m s^{- 1}

and move in the

x - y

plane with a constant acceleration of

(8 \hat{i} + 2 \hat{j}) m s^{- 2}

. At an instant when the

x -

coordinate of the particle is

16 m, y

-coordinate of the particle is:

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A mosquito is moving with a velocity $\vec{v} = 0.5 t^{2} \hat{i} + 3 t \hat{j} + 9 \hat{k} m s^{- 1}$ and accelerating in uniform conditions. What will be the direction of mosquitoes after $2 s$ ?

MEDIUM

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

Two bodies were thrown simultaneously from the origin: one straight up and the other, at an angle,

60 °

to the vertical. The initial velocity of each body is equal to

10 m s^{- 1}

Neglecting the air resistance, the distance between the two bodies after

t = 2 s

is (

Use g = 10 m s^{- 2}

)

HARD

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A balloon is moving up in air vertically above a point $A$ on the ground. When it is a height $h_{1},$ a girl standing at a distance d (point B) from A (see figure) sees it at an angle $45 °$ with respect to the vertical. When the balloon climbs up a further height $h_{2}$ , it is seen at an angle $60 °$ with respect to the vertical if the girl moves further by a distance $2.464 d$ (point C). Then the height $h_{2}$ is (given $\tan 30 ° = 0.5774$ ):

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EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

Starting at time

t = 0

from the origin with speed

1 m s^{- 1}

, a particle follows a two-dimensional trajectory in the

x - y

plane so that its coordinates are related by the equation

y = \frac{x^{2}}{2}

. The

x

and

y

components of its acceleration are denoted by

a_{x}

and

a_{y}

, respectively. Then

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

t = 0,

a particle starts moving from the origin with the velocity,

5.01 m s^{- 1}

, it moves in

x - y

plane due to a force having a constant acceleration of

(2.0 \hat{i} + 3.0 \hat{j}) m s^{- 2}

. Find the coordinate of the particle at

t = 6 s

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

The position vector of the particle is

r (t) = a \cos ω t \hat{i} + a \sin ω t \hat{j}

, where

a

and

ω

are real constants of suitable dimensions. The acceleration is

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A particle is moving in

x y

-plane crosses the origin at time

t = 0 .

The equation of motion of the particle is

y = 4 x^{2} .

If the velocity of the particle is

\vec{v} = (2 \hat{i} + 2 \hat{j}) m s^{- 1}

and acceleration is

\vec{a} = (a \hat{j}) m s^{- 2}

, then the magnitude of

a

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A bird flies at an angle of

60 °

to the horizontal. Its horizontal component of velocity is

10 m / s

. Find its vertical component of velocity in

m / s

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A particle leaves the origin with initial velocity

\vec{v} = (3 \hat{i}) m s^{- 1}

and a constant acceleration

\vec{a} = (- 1 \hat{i} - 0.5 \hat{j}) m s^{- 2}

. The position vector of particle, when it reaches its maximum

x

-coordinate, is

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

At time

t = 0

a particle starts travelling from a height

7 \hat{z} cm

in a plane keeping

z

coordinate constant. At any instant of time, it's position along the

x

and

y

directions are defined as

3 t

and

5 t^{3}

respectively. At

t = 1 s

acceleration of the particle will be

MEDIUM

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

The y-component of vector

\vec{A}

+ 3.0 m

. If A makes an angle of

30 °

counter-clockwise from the positive

y

- axis, the magnitude of

\vec{A}

is (assume

\vec{A}

is in

x - y

plane)

MEDIUM

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A particle moving in a gravity free space along horizontal with a velocity

1 m s^{- 1}

is subjected to an acceleration

(2 \hat{i} + 4 \hat{j}) m s^{- 2}

. Then the vertical distance covered by the particle by the time it covers a horizontal distance

6 m

EASY

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A person walks

25 °

north of east for

3.18 km

. How far would she have to walk due north and then due east to arrive at the same location?

MEDIUM

Physics>Mechanics>Motion in a Plane>Graphical Representation of Motion

A ball is thrown horizontally from a height with a certain initial velocity at time

t = 0

. The ball bounces repeatedly from the ground with the coefficient of restitution less than

1

as shown.

Neglect air resistance and taking the upward direction as positive, which figure qualitatively depicts the vertical component of the ball's velocity

(v_{y})

as a function of time

(t)

What is Dimensional Formula of Acceleration and its Derivation?

Important Questions on Motion in a Plane

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