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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An object is moving with variable speed, then

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Important Questions on Kinematics

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General Science>Physics>Kinematics>Speed, Velocity and 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-

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General Science>Physics>Kinematics>Speed, Velocity and Acceleration

In the following passage there are blanks, each of which has been numbered. There are questions given below the passage and for each question, four words are suggested, one of which fits the blank appropriately. Find out the appropriate word in each case.

Whenever I go into a bank, I feel scared. Everybody and everything that I see there (1) ____ me. As for the manager the sight (2) ____ him simply terrifies me and (3) ____ me want to runaway (4) _____ I can. As soon as I (5) ____ the door of the bank I lose my head (6) ____ when I try to do any (7) ____ there, I behave like an idiot. I cannot explain (8) ____ for this but that is how it (9) ____ has been that is how it is (10) ____.

Select the most appropriate option for blank No. 10.

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General Science>Physics>Kinematics>Speed, Velocity and Acceleration

A particle is moving along with

X

-axis such that its acceleration is proportional to the displacement from the equilibrium position and they are in the same direction. The displacement

x (t)

is given by (where

ω > 0

is a constant)

MEDIUM

General Science>Physics>Kinematics>Speed, Velocity and 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

MEDIUM

General Science>Physics>Kinematics>Speed, Velocity and 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

HARD

General Science>Physics>Kinematics>Speed, Velocity and 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

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General Science>Physics>Kinematics>Speed, Velocity and Acceleration

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

(v)

vs time

(t)

MEDIUM

General Science>Physics>Kinematics>Speed, Velocity and Acceleration

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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General Science>Physics>Kinematics>Speed, Velocity and 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:

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General Science>Physics>Kinematics>Speed, Velocity and 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?

HARD

General Science>Physics>Kinematics>Speed, Velocity and 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 :

MEDIUM

General Science>Physics>Kinematics>Speed, Velocity and 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

General Science>Physics>Kinematics>Speed, Velocity and 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:

MEDIUM

General Science>Physics>Kinematics>Speed, Velocity and Acceleration

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 $Q .$

HARD

General Science>Physics>Kinematics>Speed, Velocity and Acceleration

A particle of mass

m

is acted upon by a force

F

given by the empirical law

F = \frac{R}{t^{2}} v (t) .

If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

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General Science>Physics>Kinematics>Speed, Velocity and Acceleration

The position vector of a particle changes with time according to the relation

\vec{r} (t) = 15 t^{2} \hat{i} + (4 - 20 t^{2}) \hat{j} .

What is the magnitude of the acceleration at

t = 1 ?

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General Science>Physics>Kinematics>Speed, Velocity and Acceleration

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

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General Science>Physics>Kinematics>Speed, Velocity and 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?

HARD

General Science>Physics>Kinematics>Speed, Velocity and 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

General Science>Physics>Kinematics>Speed, Velocity and Acceleration

An automobile, traveling at

40 km h^{- 1}

, can be stopped at a distance of

40 m

by applying brakes. If the same automobile is traveling at

80 km h^{- 1}

, the minimum stopping distance in metres is (Assume no skidding):

An object is moving with variable speed, then

Important Questions on Kinematics

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