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

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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?

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Important Questions on Kinematics

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

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 $2 s$ ?

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

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

HARD

Physics>Mechanics>Kinematics>Motion in a Plane

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.

Question Image

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

A body of mass $2 kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) N$ It starts from rest and was at the origin initially. After $4 s$ , its new coordinates are $(8, b, 20)$ . The value of $b$ is ______.

(Round off to the Nearest Integer)

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Plane

The trajectory of a projectile projected from origin is given by the equation

y = x - \frac{2 x^{2}}{5} .

The initial velocity of the projectile is

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

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)

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

A particle moves according to the equation

x = a \sin ω t

and

y = a (1 - \cos ω t)

. The path of the particle is

HARD

Physics>Mechanics>Kinematics>Motion in a Plane

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:

HARD

Physics>Mechanics>Kinematics>Motion in a Plane

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 $\tan 30 ° = 0.5774$ ):

Question Image

HARD

Physics>Mechanics>Kinematics>Motion in a Plane

Consider a particle moving in the xy plane with velocity

\vec{v} = a \hat{i} + b x \hat{j},

where

\hat{i}

and

\hat{j}

are the unit vectors along

x

and

y

axes and

a^{'}

and

b^{'}

are constants. If the initial position of the particle is

x = y = 0,

the equation to describe the particle's trajectory in the plane is

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Plane

The position of a particle as a function of time is given by

\vec{r} (t) = A \cos ω t \hat{i} + B \sin ω t \hat{j}

where

A

and

B

are two real positive constants with

A > B

. The orbit of the particle looks like-

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

The trajectory of a projectile near the surface of the earth is given as

y = 2 x - 9 x^{2} .

If it were launched at an angle

θ_{0}

with speed

v_{0}

then

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

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Plane

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:

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Plane

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)

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

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

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Plane

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,

HARD

Physics>Mechanics>Kinematics>Motion in a Plane

Two paper screens A and B are separated by

150 m

. A bullet pierces A and then B. The hole in B is

15 cm

below the hole in A. If the bullet is traveling horizontally at the time of hitting A, then the velocity of the bullet at A is:

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

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Plane

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

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Plane

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:

EASY

Physics>Mechanics>Kinematics>Motion in a Plane

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

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?

Important Questions on Kinematics

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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?