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.

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Displacement of an object can be zero and negative.

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Important Questions on Motion in Straight Line

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

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

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

If the distance covered by a particle happens to be zero, then the displacement of the particle

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

Relation between displacement and distance covered by a moving object will be :

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

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

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

An athlete runs exactly once around a circular track of length

500 m .

The runner's displacement in the race is

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

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?

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

A boy walks

5 m

towards east and then turns at an angle of

60 °

to the north of the east and walks

5 m

. The net displacement of the boy is

HARD

Science>Physics>Motion in Straight Line>Distance and Displacement

The position of a particle as a function of time

t,

is given by

x (t) = a t + b t^{2} - c t^{3}

where

a, b

and

c

are constants. When the particle has zero acceleration, then its velocity will be:

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

A small block slides down on a smooth inclined plane, starting from rest at time

t = 0

. Let

S_{n}

be the distance travelled by the block in the interval

t = n - 1

t = n

. Then, the ratio

\frac{s_{n}}{s_{n + 1}}

is:

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

A body moves along the sides of an equilateral triangle of side

20 cm

and comes back to the intial point after one round. Then the distance and displacement of the body respectively are

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

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

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

A particle covers half of the circle of radius

r

. Then the displacement and distance of the particle are respectively

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

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

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

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?

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

A particle is moving such that its position coordinates

(x, y)

are

(2 m, 3 m)

at time

t = 0,

(6 m, 7 m)

at time

t = 2 s

and

(13 m, 14 m)

at time

t = 5 s

. The average velocity vector

({\vec{V}}_{a v})

from

t = 0

t = 5 s

is:

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

The displacement of a particle moving with uniform acceleration in time

t

is given by

S = 30 t + 5 t^{2}

, its initial velocity is _____

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

The displacement

x

(in meter) of a particle of mass

m

(in kg) moving in one dimension under the action of a force, is related to time

t

(in sec) by

t = \sqrt{x} + 3

. The displacement of the particle when its velocity is zero, will be

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

An athlete completes one round of a circular track of radius

R

40 s

. What will be his displacement at the end of

2

minutes

20

seconds?

MEDIUM

Science>Physics>Motion in Straight Line>Distance and Displacement

A bat emits an ultrasonic sound wave at

33.0 kHz

and receives an echo

0.1 s

later. What is the distance of the bat from the object-producing echo ? (Speed of sound in air is

330 m / s

)

EASY

Science>Physics>Motion in Straight Line>Distance and Displacement

A particle is moved in a semi-circular path of radius $R$ . Then

Displacement of an object can be zero and negative.

Important Questions on Motion in Straight Line

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