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 car travelled half the distance with a velocity $V$ and it covered the remaining half distance with a velocity $(\frac{V}{2})$ in the first half time and with velocity $2 V$ in the second half time. The average velocity of the car for the whole journey is

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Important Questions on Motion in a Straight Line

EASY

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

A particle covers half of the circle of radius

r

. Then the displacement and distance of the particle are respectively

HARD

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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:

EASY

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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

EASY

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

A fly is in rectilinear motion as described by the graph. The average speed of the fly is

Question Image

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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>Motion in a Straight Line>Instantaneous Velocity and Speed

The acceleration at the end of

2 s

, of a particle whose motion is represented by the equation

S = 4 t^{3} - 8 t^{2} + 5 t + 4

is ______

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

If a particle's position is given by

x = 4 - 12 t + 3 t^{2}

where

t

is in the seconds and

x

in meters. What is its velocity at

t = 1 s

? Whether the particle is moving in positive

x

direction or negative

x

direction?

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

Consider a car initially at rest, starts to move along a straight road first with acceleration

5 m s^{- 2},

then with uniform velocity and finally, decelerating at

5 m s^{- 2},

, before coming to a stop. Total time taken from start to end is

t = 25 s

. If the average velocity during that time is

72 km {hr}^{- 1},

the car moved with uniform velocity for a time of

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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>Motion in a Straight Line>Instantaneous Velocity and Speed

Consider a particle moving along the positive direction of

X

-axis. The velocity of the particle is given by

v = α \sqrt{x}

(

α

is a positive constant). At time

t = 0

, if the particle is located at

x = 0

, the time dependence of the velocity and the acceleration of the particle are respectively.

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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 _____

EASY

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

A car moves in positive

Y

-direction with velocity

v

proportional to distance travelled

y

v (y) \propto y^{β}

, where

β

is a positive constant. The car covers a distance

L

with average velocity

<v>

proportional to

L

<v> \propto L^{1 / 3}

. The constant

β

is given as

EASY

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

The displacement of a particle moving along a straight line is related to time as

\sqrt{x} = t - 3

. The displacement of the particle when its velocity is zero is

EASY

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

A bus travels at

110 km h^{- 1}

(kilometers per hour) on open highway. Its speed in metres per second is

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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:

EASY

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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?

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Instantaneous Velocity and Speed

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?

A car travelled half the distance with a velocity V and it covered the remaining half distance with a velocity V2 in the first half time and with velocity 2V in the second half time. The average velocity of the car for the whole journey is

Important Questions on Motion in a Straight Line

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A car travelled half the distance with a velocity $V$ and it covered the remaining half distance with a velocity $(\frac{V}{2})$ in the first half time and with velocity $2 V$ in the second half time. The average velocity of the car for the whole journey is