### Physics - Description of Motion in One Dimension

#### Question - 1

A stone is dropped from an ascending balloon moving with velocity $\vartheta$ at a height H.  The stone will

• A move vertical distance of $({{\vartheta^{2} \over g}+H})$
• B cover a total vertical distance of $({{\vartheta^{2} \over 2g}+H})$
• C move along a parabolic path and cover a total vertical distance of $({{\vartheta^{2} \over g}+H})$.
• D mover vertically down and cover a distance H.

#### Question - 2

Two bodies move along two perpendicular tracks at 21.6 km $h^{-1}$.  The relative velocity of one with respect to the other will be

• A 8.5 m $s^{-1}$
• B 6.5 m $s^{-1}$
• C 3.5 m $s^{-1}$
• D None of the above

#### Question - 3

A ball is thrown vertically upwards with a certain speed $\vartheta$ and is received by the thrower in 4 s.

• A Its average speed is zero.
• B Its average speed is $\vartheta$.
• C Its average velocity is 9.8 $\times$ 4 m $s^{-1}$
• D Its average velocity is always zero.

#### Question - 4

With the usual notation, for a uniformly retarded body

• A the formula s = $\vartheta$t+$1\over2$$at^{2}$ holds good
• B the formula s = ut+$1\over2$$at^{2}$ holds good
• C the formula $\vartheta$ = u + at holds good
• D the formula s = $\vartheta$t - $1\over2$$at^{2}$  holds good

#### Question - 5

A body which is uniformly accelerated changes its velocity from 20 m $s^{-1}$ to 10 m $s^{-1}$ in 5 secounds while moving in the opposite direction.  The total distance travelled in 5 s is ......... and the total displacement is .........

• A $25\over3$m and $125\over3$m
• B $100\over3$m and $75\over3$m
• C $125\over3$m and $75\over3$m
• D $75\over3$m and $25\over3$m

#### Question - 6

A rocket is to be projected vertically upwards.  It is fired with net acceleration '2g'  where is acceleration due to gravity.  After 2 minites, the fuel is exhausted.  After the fuel is exhausted, the time taken by the rocket to reach the highest point is

• A 1 minute
• B 2 minute
• C 4 minute
• D 8 minute

#### Question - 7

The displacement x of a particle moving on x-axis at any time t is given by the equation.
4t = 25 $^{+}_{-}\sqrt{100-x}$
The acceleration of the particle is

• A constant and equal to 16 m $s^{-1}$ along negative x-axis
• B constant and equal to 32 m $s^{-1}$ along negative x-axis
• C constant and equal to 32 m $s^{-1}$ along positive X-direction
• D not constant and acts along positive as well as negative X-direction depending on the magnitude of displacement x.

#### Question - 8

A tennis ball is dropped on the floor from a height of 1 m.  It rebounds to a height of 0.5 m.  If the ball was in contact with the floor for 0.01 s, the average acceleration during contact in the upward direction is

• A zero
• B 129 m $s^{-2}$
• C 442 m $s^{-2}$
• D 775 m $s^{-2}$

#### Question - 9

Choose the incorrect statement

• A A body can have zero velocity and finite acceleration
• B A body can have a constant velocity but a varying speed
• C A body can have a constant speed but a varying velocity
• D The direction of the velocity of a body can change when its acceleration is constant.

#### Question - 10

A particle moves along the X-axis such that its coordinate (x) varies with time (t) according to the expression
x = 2 - 5 t - 6 $t^{2}$
where x is in meters and t is in seconds. The initial velocity of the particle is

• A - 5 m $s^{-1}$
• B - 3 m $s^{-1}$
• C 6 m $s^{-1}$
• D 2 m $s^{-1}$