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.

HARD

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A point moves rectilinearly in one direction figure , shows the distance s traversed by the point as a function of the time t. Using the plot find: $(a)$ the average velocity of the point during the time of motion; $(b)$ the maximum velocity; $(c)$ the time moment $t_{0}$ at which the instantaneous velocity is equal to the mean velocity averaged over the first $t_{0}$ seconds.

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Important Questions on Kinematics

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

Physics>Mechanics>Kinematics>Motion in a Straight Line

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>Kinematics>Motion in a Straight Line

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>Kinematics>Motion in a Straight Line

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

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EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

In $1.0 s,$ a particle goes from $A to B$ moving in a semicircle of $1.0 m$ radius (as shown in the figure)

Question Image

The magnitude of the average velocity is

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

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 ______

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

A bus travels at

110 km h^{- 1}

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

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

The displacement-time graphs of two moving particles make angles of $30 °$ and $45 °$ with the $x$ -axis as shown in the figure. The ratio of their respective velocity is:

Question Image

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

A particle shows the distance-time curve as shown in the figure. The maximum instantaneous velocity of the particle is around the point.

Question Image

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

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>Kinematics>Motion in a Straight Line

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>Kinematics>Motion in a Straight Line

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

MEDIUM

Physics>Mechanics>Kinematics>Motion in a Straight Line

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field

\vec{E}

. Due to the force

q \vec{E}

, its velocity increases from 0 to

6 m s^{- 1}

in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between

0

3

seconds are respectively

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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>Kinematics>Motion in a Straight Line

A car covers the first half distance between two places at

40 kmph

and the other half at

60 kmph .

The average speed of the car is

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

The displacement of a body is given by

x = 4 t + 5 t^{3},

where

x

is in metre and

t

is in second. The difference between the average velocity of the body in the time-interval

t = 1 s

t = 2 s

and its instantaneous-velocity at

t = 1 s

Important Questions on Kinematics

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