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1.Distinguish between distance travelled and displacement:
Distance is a scalar quantity while displacement is a vector quantity but both having the same dimension (L) and unit metre(m).
The magnitude of the displacement of an object between two points is the shortest distance between those two points.
For a moving particle distance can never be zero or negative while displacement can be zero, positive or negative.
For a moving particle distance can never decrease with time while displacement can. Decrease in displacement with time means that the body is moving towards the initial position.
2.Define the term 'Speed':
Speed of a body is the distance travelled by unit time.
ie., speed = 
If a body travels a distance 's' in time 't', then its speed ' v ' is given by
v =
The SI unit of speed is meters per second. Speed has magnitude only, it has no specified direction, therefore speed is a scalar quantity.
3.A car driver covers a distance of 3 kilometers in 5 minutes . Calculate his speed in:
(a) centimeters per second (cm/s)
(b) meters per second (m/s) and
(c) kilometers per hour (km/h)
(a) Distance travelled = 3 km
= 3 × 1000 m
= 3 × 1000 × 100 cm
= 3,00, 000 cm
Time taken = 5 minutes
= 5 × 60 seconds
= 300 s
We have, speed =
= 
= 1000 cm ⁄ s
(b) Distance travelled = 3km
= 3 × 1000 m
= 3000 m
Time taken = 5 minutes
= 5 × 60 seconds
= 300 s
speed = 
= 10 m ⁄ s
(c) Distance travelled = 3 km
Time taken = 5 minutes
4.Distinguish between speed and velocity:
Speed is the rate of change of position ; but velocity is rate change of displacement.
Both speed and velocity have the same unit and dimensions.
Speed is a scalar quantity while velocity is a vector quantity.
Velocity can be positive or negative but speed can only be positive.
Speed is greater than or equal to the velocity.
5.The train 'A' travelled a distance of 120 km in 3 hours where as another train 'B' travelled a distance of 180 km in 4 hours. Which train travelled faster?
In order to solve this problem, we have to calculate the speeds of both the trains separately. The train having higher speed will have travelled faster.
We have speed = Distance travelled / Time taken
Distance travelled by train A = 120 km
Time taken by train A = 3 h
So,
Speed of train A =
= 40 km/h
Distance travelled by train B = 180 km
Time taken by train B = 4 h
Speed of train B = 
= 45 km/h
Since the speed of train B is higher, therefore, the train B has travelled faster.
6.What do you mean by Uniform Velocity (or Constant Velocity)?
A body has a uniform velocity if it travels in a specified direction in a straight line and moves over equal distances in equal intervals of time, no matter how small these intervals may be.
7.What is acceleration?
Acceleration of a body is defined as the rate of change of velocity with time.
ie., Acceleration = change in velocity / Time taken for change
Change in velocity is the difference between the final velocity and initial velocity.
Suppose the initial velocity of a body is 'u' and it changes to a final velocity ' v' in time t, then:
where
a is the acceleration of the body
v is the final velocity of the body
u is the initial velocity of the body
The SI unit of acceleration is meter per second per second or m / s2. Acceleration is a vector quantity.
8.Differentiate between Uniform Acceleration and Non-Uniform Acceleration: Give example:
A body has a uniform acceleration if it travels in a straight line and its velocity increases by equal amounts in equal intervals of time. In other words, a body has a uniform acceleration if its velocity changes at a uniform rate.
Here are some examples of the uniformly accelerated motion :
The motion of a freely falling body is an example of uniformly accelerated motion.
The motion of a ball rolling down an inclined plane is an example of uniformly accelerated motion.
A body has a non-uniform acceleration if its velocity increases by unequal amounts in equal intervals of time. In other words, a body has a non-uniform acceleration if its velocity changes at a non-uniform rate.
The speed (or velocity) of a car running on a crowded city road changes continuously. At one moment the velocity of a car increases whereas at another moment it decreases. So, the movement of the car on a crowded city road is an example of non-uniform acceleration.
9.What is meant by Retardation?
Acceleration takes place when the velocity of a body changes. The velocity of a body may increase or decrease, accordingly the acceleration is of two types- positive acceleration and negative acceleration. If the velocity of a body increases, the acceleration is positive and if the velocity of a body decreases, the acceleration is negative. Negative Acceleration is also known as Retardation or Deceleration.
Retardation is measured in the same way as acceleration, that is retardation is equal to 
and has the same units of acceleration ( "m ⁄ s2).
Example : Train comes to rest at the station.
10.A driver decreases the speed of a car from 25 m/s to 10 m/s in 5 seconds. Find the acceleration of the car?
Initial velocity of car, u = 25 m/s
Final velocity of car, v = 10 m/s
Time taken, t = 5 s
Thus, the acceleration of car is -3m/s2. The negative sign of acceleration means that it is retardation.
We can also say that the car has a retardation of +3m / s2
11. Derive the first equation of motion , v = u + at:
First equation of motion :
The first equation of motion is v = u + at
It gives the velocity acquired by a body in time t. Let's derive this first equation of motion.
Consider a body having initial velocity 'u' .Suppose it is subjected to a uniform acceleration 'a' so that after time 't' its final velocity becomes ' v'. Now, from the definition of acceleration we know that :
where v = final velocity of the body,
u = initial velocity of the body,
a = acceleration, and
t = time taken.
12.Derive the second equation of motion, s = ut + 
at2
Second equation of motion:
The second equation of motion is s = ut + 
at2 . It gives the distance travelled by a body in time 't'.
Suppose a body has an initial velocity 'u' and a uniform acceleration 'a' for time 't' so that its final velocity becomes ' v'. Let the distance travelled by the body in this time be 's'. The distance travelled by a moving body in time 't' can be found out by considering its average velocity. Since the initial velocity of the body is 'u' and its final velocity is ' v', the average velocity is given by :
Average velocity = 
= 
Also, Distance travelled = Average velocity × Time
So, s = 
Putting the first equation of motion in the above equation, we get :
where s is the distance travelled by the body in time t
u is the initial velocity of the body
a is acceleration.
13.Derive the third equation of motion, v2 = u2 + 2 a s:
Third equation of motion
The third equation of motion is v2 = u2 + 2as. It gives the velocity acquired by a body in travelling a distance 's'.
The third equation of motion can be obtained by eliminating 't' between the first two equations of motion.
From the second equation of motion we have:
s = ut + at2 →(1)
And from the first equation of motion we have :
v = u + at →(2)
Putting this value of t in equation (1) we get
2as = v2 - u2
or v2 = u2 + 2as
where v = final velocity
u = initial velocity
a = acceleration
s = distance travelled.
Practice in Related Chapters |
| Motion and Liquids |
| Sound |
| Work, Power, Energy and Heat |
| Measuring Instrument |
