MEDIUM

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Derive the dimensional formula of the acceleration.

Important Questions on Motion in a Straight Line

HARD

Physics>Mechanics>Motion in a Straight Line>Acceleration

The relation between time

t

and distance

x

for a moving body is given as

t = m x^{2} + n x

, where

m

and

n

are constants. The retardation of the motion is: (When

v

stands for velocity)

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Acceleration

The relation between time

t

and distance

x

for a moving particle is

t = α x^{2} + β x,

where

α

and

β

are constants. If

v

is the velocity at distance

x

, then the retardation of the particle is

EASY

Physics>Mechanics>Motion in a Straight Line>Acceleration

The variation of speed

(in m / s)

of an object with time (in seconds) is given by the expression

V (t) = V_{0} - 5 t + 5 t^{2}

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Acceleration

A body starts from rest with uniform acceleration and moves in a straight line. If its speed after

n

seconds is

v

, then the distance covered in the last

2 s

is:

EASY

Physics>Mechanics>Motion in a Straight Line>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 ?

EASY

Physics>Mechanics>Motion in a Straight Line>Acceleration

A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following a ________

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Acceleration

The driver of a bus moving at an speed of

60 km {hr}^{- 1}

saw a man at a distance of

52 m

from the bus. The driver stopped the car at a distance of

2 m

from the man using brake. The time required to stop the bus is

EASY

Physics>Mechanics>Motion in a Straight Line>Acceleration

A ball is dropped vertically from height $h$ and is bouncing elastically on the floor (see figure). Which of the following plots best depicts the acceleration of the ball as a function of time.

Question Image

EASY

Physics>Mechanics>Motion in a Straight Line>Acceleration

An aircraft is moving with uniform velocity

150 m s^{- 1}

in the space. If all forces acting on it are balanced, then it will

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Acceleration

Starting from the origin at time

t = 0

, with initial velocity

5 \hat{j} m s^{- 1}

, a particle moves in the

x

y

plane with a constant acceleration of

(10 \hat{i} + 4 \hat{j}) m s^{- 2}

. At time

t

, its coordinates are

(20 m, y m)

. The values of

t

and

y

are, respectively:

EASY

Physics>Mechanics>Motion in a Straight Line>Acceleration

The displacement of a particle moving along

x

-axis is given by

x = 8 t^{2} + 18 t .

The average acceleration during the interval

t_{1} = 2 s

and

t_{2} = 4 s

EASY

Physics>Mechanics>Motion in a Straight Line>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)

HARD

Physics>Mechanics>Motion in a Straight Line>Acceleration

A rocket lifts off from the ground and accelerates upwards at

1 m s^{- 2}

20

seconds after liftoff a piece breaks off from the bottom of the rocket. After breaking off, how much time it takes approximately to reach the ground? (Take

g = 10 m s^{- 2}

)

EASY

Physics>Mechanics>Motion in a Straight Line>Acceleration

A particle starts from rest. Its acceleration $a$ versus time $t$ is shown in the figure. The maximum speed of the particle will be:

Question Image

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Acceleration

Two cars

A

and

B

initially at rest are moving in the same direction with accelerations,

a_{1}

and

a_{2}

respectively. After a certain time, they achieve velocities

v_{1}

and

v_{2}

respectively and are separated by a distance of

50 m .

(a_{1} - a_{2}) = 4 m s^{- 2},

then the quantity

(v_{1} - v_{2})

will be

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Acceleration

What is the length of the bridge (in

m

), which a train

130 m

long and travelling at

45 km h^{- 1}

can cross in

30 s

EASY

Physics>Mechanics>Motion in a Straight Line>Acceleration

A particle moves in a plane with uniform acceleration having direction different than that of instantaneous velocity. What is the nature of trajectory?

MEDIUM

Physics>Mechanics>Motion in a Straight Line>Acceleration

The position of an object moving along

X

-axis is given as

x = a + b t^{2}

, where

a, b

are constants and

t

is time in seconds. The object covers a distance of

16 m

2 secs

. If the average velocity of the object between

t = 3 \sec

and

t = 5 s

28 m s^{- 1}

, the values of

a

and

b

are:

MEDIUM

Physics>Mechanics>Motion in a Straight Line>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:

EASY

Physics>Mechanics>Motion in a Straight Line>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?

Derive the dimensional formula of the acceleration.

Important Questions on Motion in a Straight Line

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