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.

MEDIUM

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The distance $r$ from the origin of a particle moving in $x - y$ plane varies with time as $r = 2 t$ and the angle made by the radius vector with positive $x$ -axis is $θ = 4 t$ . Here, $t$ is in second, $r$ in metre and $θ$ in radian. The speed of the particle at $t = 1 \sec$ is

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Important Questions on Kinematics

MEDIUM

Physics>Mechanics>Kinematics>Variable Acceleration

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

Physics>Mechanics>Kinematics>Variable Acceleration

A particle is moving along the positive

x

-axis as

x = a (t - 3) + b {(t - 3)}^{2} + 4 (t - 3)

, which of the following is true?

HARD

Physics>Mechanics>Kinematics>Variable Acceleration

A piece of wood of mass

0.03 kg

is dropped from the top of a

100 m

height building. At the same time, a bullet of mass

0.02 kg

is fired vertically upward, with a velocity

100 m s^{- 1},

from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is:

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

EASY

Physics>Mechanics>Kinematics>Variable Acceleration

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>Variable Acceleration

A particle is projected with velocity

v_{0}

along

x

-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e.

m a = - α x^{2} .

The distance at which the particle stops:

EASY

Physics>Mechanics>Kinematics>Variable Acceleration

A body moves along a straight line with acceleration

3 m s^{- 2}

for

2 s

and then with acceleration

4 m s^{- 2}

for

3 s.

What is his average acceleration?

MEDIUM

Physics>Mechanics>Kinematics>Variable Acceleration

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>Variable Acceleration

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

HARD

Physics>Mechanics>Kinematics>Variable Acceleration

The instantaneous velocity of a particle moving in a straight line is given as

v = α t + β t^{2}

, where

α

and

β

are constants. The distance travelled by the particle between

1 s

and

2 s

is:

MEDIUM

Physics>Mechanics>Kinematics>Variable Acceleration

If the velocity of a body related to displacement

x

is given by

v = \sqrt{5000 + 24 x} m s^{- 1},

then the acceleration of the body is _________

m s^{- 2} .

EASY

Physics>Mechanics>Kinematics>Variable Acceleration

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity

(v)

vs time

(t)

EASY

Physics>Mechanics>Kinematics>Variable Acceleration

If the velocity of a particle is

υ = A t + B t^{2}

, where

A

and

B

are constants, then the distance travelled by it between

1 s

and

2 s

is:

HARD

Physics>Mechanics>Kinematics>Variable Acceleration

A parachutist with total weight

75 kg

drops vertically onto a sandy ground with a speed of

2 m s^{- 1}

and comes to a halt over a distance of

0.25 m

. The average force from the ground on her is close to-

EASY

Physics>Mechanics>Kinematics>Variable Acceleration

In a car race on straight road, car

A

takes a time

t

less than car

B

at the finish and passes finishing point with a speed

v

more than that of car

B .

Both the cars start from rest and travel with constant acceleration

a_{1}

and

a_{2}

respectively. Then $v$ is equal to:

HARD

Physics>Mechanics>Kinematics>Variable Acceleration

A stone thrown down with a seed

u

takes a time

t_{1}

to reach the ground, while another stone, thrown upwards from the same point with the same speed, takes time

t_{2}

. The maximum height the second stone reaches from the ground is

MEDIUM

Physics>Mechanics>Kinematics>Variable Acceleration

A bullet loses

{(\frac{1}{n})}^{th}

of its velocity passing through one plank. Considering uniform retardation, the number of such planks that are required to stop the bullet can be:

HARD

Physics>Mechanics>Kinematics>Variable Acceleration

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path.The relation between H, u and n is :

EASY

Physics>Mechanics>Kinematics>Variable Acceleration

The displacement of a particle starting from rest at

t = 0

is given by

s = 9 t^{2} - 2 t^{3}

. The time in seconds at which the particle will attain zero velocity is

MEDIUM

Physics>Mechanics>Kinematics>Variable Acceleration

A particle is moving with speed

v = b \sqrt{x}

along positive

x -

axis. Calculate the speed of the particle at time

t = τ

(assume that the particle is at origin at

t = 0

)

HARD

Physics>Mechanics>Kinematics>Variable Acceleration

A particle undergoes a one-dimensional motion such that its velocity varies according to $v (x) = β x^{- 2 n}$ , where $β$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by

The distance r from the origin of a particle moving in x-y plane varies with time as r=2t and the angle made by the radius vector with positive x-axis is θ=4t. Here, t is in second, r in metre and θ in radian. The speed of the particle at t=1 sec is

Important Questions on Kinematics

Learn and Prepare for any exam you want !

The distance $r$ from the origin of a particle moving in $x - y$ plane varies with time as $r = 2 t$ and the angle made by the radius vector with positive $x$ -axis is $θ = 4 t$ . Here, $t$ is in second, $r$ in metre and $θ$ in radian. The speed of the particle at $t = 1 \sec$ is