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

Earn 100

A ball is projected vertically upward with an initial velocity of $50 m s^{- 1}$ at $t = 0 s$ . At $t = 2 s$ , another ball is projected vertically upward with same velocity. At $t =$ _____ $s$ , second ball will meet the first ball $(g = 10 m s^{- 2})$ .

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Important Questions on Motion in a Straight Line

EASY

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

Directions: Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.

Every rash driver becomes a ____ killer.

EASY

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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

(v)

vs time

(t)

HARD

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Kinematic Equations for Uniformly Accelerated Motion

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>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Kinematic Equations for Uniformly Accelerated Motion

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:

EASY

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

Two sentences are given below and you are required to find the correct sentence which combines both the sentences.

Which is the correct combination of the given two sentences?

He is too tired. He could not stand.

EASY

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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:

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

In the following sentence, a blank space with four options is given. Select whichever preposition or determiner you consider the most appropriate for the blank space.

These are the good rules to live _____.

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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

HARD

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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

EASY

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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

Physics>Mechanics>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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>Motion in a Straight Line>Kinematic Equations for Uniformly Accelerated Motion

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 projected vertically upward with an initial velocity of 50 m s-1 at t=0 s. At t=2 s, another ball is projected vertically upward with same velocity. At t= _____ s, second ball will meet the first ball g=10 m s-2.

Important Questions on Motion in a Straight Line

Learn and Prepare for any exam you want !

A ball is projected vertically upward with an initial velocity of $50 m s^{- 1}$ at $t = 0 s$ . At $t = 2 s$ , another ball is projected vertically upward with same velocity. At $t =$ _____ $s$ , second ball will meet the first ball $(g = 10 m s^{- 2})$ .