UNIFORM MOTION (NUMERICALS) ASSIGNMENT

A body is dropped from the top of a tower and falls freely. The distance covered by it after n seconds is directly proportional to

n^{2}

2 n - 1

2 n^{2} - 1

in q. 1 the velocity of the body after n seconds is proportional to

2 n - 1

2 n^{2} - 1

A ball dropped from a height h reaches the ground in time T. what is its height at time

T / 2

h / 8

h / 4

h / 2

3 h / 4

The distance time graph of a particle at time t makes an angle

45^{\circ}

with the time axis. After one seconds it makes an angle

60^{\circ}

with the tie axis. What is the acceleration of the particle.

\sqrt{} 3 - 1

\sqrt{} 3 + 1

\sqrt{3}

A car accelerates from rest at

5 m s^{- 2}

and then retards to rest at

3 m^{- 2}

2.the maximum velocity of the car is

30 m s^{- 2}

what is the distance covered by the car ?

150 m

240m

300 m

The displacement time graph for the two particles A and B are straight lines inclined at angles

30^{0}

and

60^{\circ}

with the time axis. The ratio of the velocities

V_{A} : V_{B}

will be

1:2

1:√3

√3:1

1:3

The velocity 'u' of the body moving along a straight line with constant retardation 'a' reduces by 75% in time t. what is the time taken in doing so ?

u / 4 a

3 u / 4 a

4 u / 3 a

The acceleration of the particle, starting from rest, varies with time according to the relation:

a = - A ω^{2}

sin t.the displacement of this particle at a time t will be

- (1 / 2) (A ω^{2} s i n ω t) t^{2} .

(Ao sin ot).

(Ao cos ot)t.

A sin ot.

A particle is moving eastwards with a velocity of

5 m / s

. in 10 seconds the velocity changes to

5 m / s .

northwards. The average acceleration in this time is

Zero

1 / \sqrt{} 2 m / s^{2} .

towards north-west.

a car can be stopped over a distance x when its momentum is '

p^{'}

. what will be the stopping distance when the momentum is 2p.

8x.

The displacement x and time t are related as

t = p x^{2} + q x + r

when p,q,r, are constants. What is the relation between velocity v and the acceleration a?

a \propto v

a \propto v^{2}

The distance covered by a particle moving on a straight line path at any instant is given by

t = a x^{2} + b x .

if the instantaneous velocity of the particle be v. What is the acceleration of the particle.

2 a v^{3}

- 2 a v^{3} .

2 a v^{2}

- 2 a v^{2}

A particle moves so that the displacement x at time t is given by

x^{2} = 1 + t^{2}

t2.what is its acceleration.

1 / x

t^{2} / x^{3}

A car starts from rest and moves with constant acceleration. The ratio of the distance covered in the nth second to that in n seconds is:

1 / 2 n^{2} - 1 / n

1 / 2 n^{2} + 1 / n

2 / n - 1 / n^{2}

2 / n + 1 / n^{2}

The height y and the distance x along the horizontal plane of a projectile on a certain planet are given by

y = (8 t - 10 t^{2})

meter and

x = 6 t m e t e r

where t is in seconds. the velocity with which the projectile is projected, is:

8 m / s

6 m / s

10 m / s

not obtained from data

the position

(x & y)

co-ordinates of particle at the instant t are

\sqrt{21}

t and

. respectively. What is the initial speed of the particle

3 m / s

4 m / s

5 m / s

A shell is fired from a cannon with a velocity

V m / s

at an angle with the horizontal direction. At the highest point in its path explodes into two pieces of equal mass. one of the pieces retraces its path to the canon then the speed of the other piece immediately after explosion is :

3V cos

2 V c o s θ

3 / 2 \lor c o s θ

\sqrt{} 3 / 2 c o s θ

A train starts from the rest ad acquires with a speed v with uniform acceleration . Then it comes to stop with uniform retardation . What will be the average velocity of the train?

α β / (α + β)

(α + β) / α β

v / 2