BS Physics (Foundation) Series

1. 1
Module # 03
Speed & Velocity
Speed
Speed is the ratio of total distance covered to the total time taken.
Speed is usually denoted by V. If distance is denoted by S and
time by t, then, it is written as:
V = S/t
Units of speed are meter per second or kilo meter per hour.
Speed has no direction. It is a scalar quantity. The speedometer
of a moving car measures speed of the car.
The terms speed and velocity are commonly used
interchangeably, but, by definition, there is an important difference
between these two terms. Speed is always determined by
distance and velocity is determined by displacement. Hence,
speed is a scalar quantity and velocity is a vector quantity.
Average Speed
The average speed is defined as the total distance covered
divided by the total time with varying speeds.
If average speed is denoted by Vav, then

2. 2
Total distance covered S
Vav = ------------------------------ = ------
Total time t
Uniform Speed or Constant Speed
If the body covers equal distances in equal intervals of time, its
motion is said to be uniform speed.
The speed is said to be constant or uniform, if the moving body
covers equal distances in equal intervals of time however small.
Velocity
The rate of change of displacement is called velocity. It is a vector
quantity. If the change in displacement is ΔS, taking place in time
Δt, then, the velocity is given as
Displacement ΔS
Velocity = V = -------------------- = -------------
Time Δt
The units of velocity are m/s or km/h in a particular direction.

3. 3
Constant Velocity
If a body covers equal displacements in equal intervals of time,
then, the body moves with constant velocity. The body moving
with constant velocity has no acceleration and we say that the
motion of the body is uniform motion.
Instantaneous Velocity
The velocity of a body for very short interval of time (instant) is
called the instantaneous velocity. A very short interval of time
means that Δt is too short that Δt tends to zero (or Δt approaches
to zero). The velocity of a body for any instant is called the
instantaneous velocity and it is denoted as Vinst.
Therefore,
ΔS
Instantaneous Velocity = Vins. = Lim -------------
Δt0 Δt
Average Velocity
If a body is moving with variable velocity, then, to find average
velocity, we divide the total displacement by total time.

4. 4
Therefore,
Total Displacement ΔS
Average Velocity = Vaverage = ---------------------------- = ------------
Total time Δt
Uniform Velocity
If the velocity is uniform, both average and instantaneous
velocities are equal. The displacement - time graph of a body
moving with uniform velocity will be a straight line.
The velocity is said to be constant or uniform, if the moving body
covers equal displacements in equal intervals of time, however
small.
Variable Velocity or Non-Uniform Velocity
If a body covers unequal displacements in equal intervals of time,
then, the body will be moving with variable velocity. The body has
non-uniform velocity. The body may have positive or negative
acceleration. A body falling freely has variable velocity.
Thus, if the displacements covered by a body in equal intervals of
time are not equal, then, the body is said to move with variable
velocity i.e. its speed or direction or both are changing e.g.
velocity of a body moving in a circle.

5. 5
Terminal Velocity
It is the maximum velocity VT at which the net acceleration
becomes zero.
OR
Terminal velocity is that maximum velocity at which the weight of
a body becomes equal to the drag force.
Escape Velocity
It is defined as the initial velocity given to a body on the surface of
the earth which will enable the body to escape out of the influence
of the earth's gravitational field. Thus, the body will be able to go
up to infinity.
Angular Velocity
The angular displacement per second is called angular velocity. It
is dented by . Therefore,
Angular displacement 
Angular Velocity =  = --------------------------------- = -----------
time t

6. 6
Direction of Angular Velocity
The angular velocity  is a vector quantity. Its direction is given by
right hand rule.
Units of Angular Velocity
The SI units of angular velocity are radian per second or written
as rads-1
.
Other Units are revolution per second or written as revs-1
and
degrees per second or written as degs-1
.
Instantaneous Angular Velocity
If the angular velocity is not uniform during the interval of time 't',
then, we can find the instantaneous angular velocity at any instant
which is defined as the angular displacement in a very small
interval of time.
OR
The angular velocity at a particular instant is called instantaneous
angular velocity.

7. 7
Average Angular Velocity
The average angular displacement per second is called average
angular velocity. It is dented by .
Thus,
Average angular displacement ()
Average Angular Velocity =  = -----------------------------------------------------------
Time
Revolving Velocity
The velocity with which artificial satellites revolve around the earth
is called revolving velocity.