# Question-1

**Define Kinematics?**

**Solution:**

The branch of Physics which deals with the study of mechanical motion of bodies without considering the forces that cause this motion is called Kinematics.

# Question-2

**What is meant by â€˜point objectâ€™ in Physics?**

**Solution:**

An object is referred to as a point object if its dimensions are negligible when compared to the distance travelled by it.

# Question-3

**Can a body have zero velocity but still possess acceleration?**

**Solution:**

Yes, when a body is projected upwards, at the highest point its velocity is zero but the acceleration is g.

# Question-4

**Under what conditions the distance covered by a particle is equal to the magnitude of displacement of the particle?**

**Solution:**

The distance covered by a particle is equal to the magnitude of displacement of the particle when the body moves with constant velocity.

# Question-5

**Is it possible that the average velocity of a particle is zero when its average speed is not zero?**

**Solution:**

When a particle returns to the starting point, its average velocity is zero even as its average speed is not zero.

# Question-6

**Can a particle in one dimensional motion with zero speed have non-zero velocity?**

**Solution:**

No. A particle in one dimensional motion with zero speed may not have non-zero velocity because, speed of a body is equal to magnitude of its velocity.

# Question-7

**What will be the nature of x-t graph for a uniform motion?**

**Solution:**

The nature of x-t graph for uniform motion will be a straight line, inclined with time axis.

# Question-8

**A car is moving along a straight road at a speed of 120km/h. By applying brakes, it is brought to rest within a distance of 250m. Calculate the retardation of the car and the time in which it comes to rest.**

**Solution:**

Initial velocity of car,

U = 120km/h = 33.33ms^{-1}

As the car finally comes to rest,

Final velocity of car, v = 0

Distance travelled, s = 250m,

V^{2} - u^{2} = 2as

(0)^{ 2} - (33.33)^{ 2} = 2a Ã— 250

a = -2.22ms^{-2}

-ve sign shows that acceleration is negative, which is retardation.

Now, v = u + at

0 = 33.33ms^{-1} + 2.22ms^{-2}t

t = 15s.

# Question-9

**What does slope of x-t graph represent?**

**Solution:**

Slope of x-t graph represents velocity of the object.

# Question-10

**What will be nature of x-t graph for a uniform motion?**

**Solution:**

The nature of x-t graph will be a straight line, inclined with time-axis.

# Question-11

**Two stones of different sizes are dropped simultaneously from the top of a building. Which stone would reach the ground earlier? Why?**

**Solution:**

Both the stones would reach the ground simultaneously as the force exerted by the gravity of the earth on both the stones will be almost the same.

# Question-12

**A ball, after having fallen from rest under the influence of gravity for 5s, crashes a horizontal glass plate, thereby losing 1/3 of its velocity. If it then reaches the ground in 3s, find the height of the plate above the ground.**

**Solution:**

u = 0,a = g = 9.8 ms

^{-2},t = 5 s, v = ?

V = u + gt

= 0 + 9.8 Ã— 5

= 49.0 ms^{-1 }

When the ball crashes the glass plate its velocity becomes = 2v/3 = 2(49-0) ms^{-1}.

Now, we will find the height travelled by the ball in time 3 s moving with 32.67 ms^{-1}.

h = ut + (1/2) gt^{2 }

= 32.67(3) + (1/2)(9.8)(3)^{2 }

= 98.01 +44.1

h = 142.11 m.

# Question-13

**A bomb is dropped from a aircraft when it is directly above a target at a height of 1000m. The aircraft is moving with a velocity of 500km/h. Will the bomb hit the target? If not, by how much distance will the bomb miss the target?**

**Solution:**

s = 1000m

V(0) = 0, g = 9.8 m/s^{2 }

âˆ´s = v(0)t + (1/2)gt^{2 }

1000 = 0+(1/2) Ã— 9.8 Ã— t^{2 }

t^{2 }= (2000/9.8) or t= (100/7)s

Horizontal velocity of the bomb=Velocity of the aircraft

Or v = 500 km/h = (500 Ã— 1000)/(60 Ã— 60)=1250/9 m/s

Therefore, distance between the bomb and the target

= vt

= (1250 Ã—100)/(9 Ã—7)

= 1984 m

= 1.984 Km.

# Question-14

**Two trains A and B of length 500 m each are moving in two parallel tracks with a uniform speed of 56 Km/h in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 2 ms**

^{-2}. If after 25 s, the guard of B just brushes past the driver of A, what was the original distance between them?**Solution:**

Relative velocity (initial) of B w. r. t. A = 0

i.e., u = 0, a=2 ms^{-2}, t=25 s

s = ut + (1/2)at^{2 }

s = 0 + (1/2)(2 ms^{-2})(25 s)^{2 }

= 625 m.

Original distance between them = 625 m.

# Question-15

**It is the velocity and not the acceleration which decides the direction of motion of a body." Justify this statement with help of a suitable example.**

**Solution:**

The direction of velocity is always in the direction of motion of the body, whereas the direction of acceleration may or may not be in the direction of the motion of the body. Hence, the velocity decides the direction of motion of the body.

Example: When a ball is thrown vertically upward, then the direction of motion of the ball and velocity is same i.e., upward. On the other hand the acceleration due to gravity acts downwards the earth. Thus the direction of the acceleration is opposite to the direction of motion of the ball.

# Question-16

**A boy leaves his home and goes on a car, returning to his home after traveling 20 km in half an hour. What is his average displacement?**

**Solution:**

The displacement is zero, because the initial and final positions are same.

# Question-17

**The front screen of a moving car may get wet, even when the raindrops are falling vertically downwards.**

**Solution:**

The relative velocity of the rain-drops is inclined towards the wind screen.

# Question-18

**Two balls of different masses (one lighter and other heavier) are thrown vertically upward with same initial speed. Which one rises to greater height?**

**Solution:**

When the two balls are thrown vertically upward, the balls will rise to the same height. It is because for a body moving with given initial velocity and acceleration, the distance covered by the body does not depend on the mass of the body.

# Question-19

**Can a body be said to be at rest as well as in motion at the same time?**

**Solution:**

Yes. Rest and motion are relative terms. A body at rest with respect to one object may be in motion with respect to another object. For example, a person sitting in a moving bus is at rest with respect to other passengers in the bus at the same time he is in motion with respect to a building on the roadside.

# Question-20

**A particle travelling along a straight line traversed oneâ€“third of the total distance with a velocity**

**Î½**

_{0}. The remaining part of the distance was covered with a velocity Î½_{1 }for half the time and with velocity Î½

_{2 }for the other half of the time. Find the mean velocity of the point averaged over the whole time of motion.**Solution:**

Let the time taken for first one-third distance be t

_{1}, then t

_{1 }= d/3Î½

_{0 }where d is the total length of the journey.

Let, the time taken for next 2d/3 distance be t^{2}, then,

or t_{2} =

Thus, the total time taken for the journey is

Thus the average velocity =

v =

# Question-21

**A ball is thrown vertically upward. After some time it returns back to earth. Draw speed-time graph for the ball. Neglect air resistance.**

**Solution:**

When a ball is thrown vertically upward, it has some initial speed. As it goes up, its speed decreases and becomes zero at the highest point. From the highest point it starts the downward journey. The speed goes on increasing and becomes equal to the initial speed when the ball reaches the ground.

The speed-time graph for the motion of the ball is shown in figure below

# Question-22

**Why does a person sitting in one train think that the other train is at rest, when both the trains are moving on parallel tracks with the same speed and in the same direction?**

**Solution:**

This is because the relative velocity of the train in which the person is sitting with respect to the other train is zero.

For example, let the velocity of the train A, v = 50 km/hr due east

Similarly velocity of the train B, v = 50 km/hr due east

âˆ´ Relative velocity of train A w.r.t. train B is = 50 - 50 = 0.

# Question-23

**Is it true that a body along a straight line with positive value of acceleration always be speeding up?**

**Solution:**

No, it is not. If a body is thrown vertically upwards, its velocity is directed upward but the acceleration due to gravity is directed downwards and the body speeds down. If the downward direction is taken as positive, the acceleration will be positive but the velocity is negative. Thus, if the velocity is negative, the body will speed up when subjected to a positive acceleration.