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 ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $\frac{d}{2}$ . Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground as

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Important Questions on Kinematics

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Physics>Mechanics>Kinematics>Motion in a Straight Line

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 $Q .$

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

(v)

vs time

(t)

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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-

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

Physics>Mechanics>Kinematics>Motion in a Straight Line

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>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

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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)

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

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Physics>Mechanics>Kinematics>Motion in a Straight Line

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:

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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?

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Physics>Mechanics>Kinematics>Motion in a Straight Line

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:

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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?

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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>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

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x - a x i s$ . Identify all figures that correctly represent the motion qualitatively.
( $a =$ acceleration, $v =$ velocity, $x =$ dispalcement, $t =$ time)
$(A)$ Question Image
$(B)$
$(C)$
$(D)$

EASY

Physics>Mechanics>Kinematics>Motion in a Straight Line

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 ?

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?

HARD

Physics>Mechanics>Kinematics>Motion in a Straight Line

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>Motion in a Straight Line

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):

A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d2. Neglecting subsequent motion and air resistance, its velocity v varies with the height h above the ground as

Important Questions on Kinematics

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A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $\frac{d}{2}$ . Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground as