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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A man travels a distance of $20 km$ from his home to office, and $10 km$ towards his house back. Then the displacement covered by the man in the whole trip is

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Important Questions on Motion in a Straight Line

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

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 $Q .$

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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:

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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

)

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

Motion of a particle in

x - y

plane is described by a set of following equations

x = 4 \sin (\frac{π}{2} - ω t) m

and

y = 4 \sin (ω t) m

. The path of the particle will be

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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?

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

When a particle moves with variable velocity, which of the following statement are NOT correct ?
(i) Average speed = average velocity
(ii) Instantaneous speed = instantaneous velocity
(iii) Distance covered = magnitude of displacement

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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?

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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?

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length 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

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

An athlete runs exactly once around a circular track of length

500 m .

The runner's displacement in the race is

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Physics>Mechanics>Motion in a Straight Line>Position, Path Length and Displacement

A particle covers half of the circle of radius

r

. Then the displacement and distance of the particle are respectively

A man travels a distance of 20 km from his home to office, and 10 km towards his house back. Then the displacement covered by the man in the whole trip is

Important Questions on Motion in a Straight Line

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A man travels a distance of $20 km$ from his home to office, and $10 km$ towards his house back. Then the displacement covered by the man in the whole trip is