Speed And Velocity SS1 Physics Lesson Note

Speed: Speed is defined as the rate of change of distance moved in an unspecified direction or the rate of change of distance per unit time in an unspecified direction. It is measured in metres per second (m/s). It is a scalar quantity.

The mathematical expression of speed is Speed = distance moved ÷ time 

Average Speed: Average speed is defined as the ratio of the total distance travelled to the total time taken. It is a scalar quantity and measured in m/s or ms-1

This, average speed = total distance travelled ÷ total time taken

When a body covers an equal distance in equal time intervals, no matter how small the time interval may be, it is said to be a uniform speed or constant speed.

Velocity: Velocity is defined as the rate of change of distance moved in a specific direction or the rate of change of displacement. Velocity is a vector quantity. For instance, it would be easy and correct to say that a car travelling at a steady speed of 50km/h in a direction of N40oE has a velocity of 50km/h, N40°E.

 velocity = displacement ÷ time

          Graph of uniform velocity

Uniform (constant) velocity: An object is said to undergo (constant) velocity, if the rate of change of displacement is constant, no matter how small the interval may be.

Example 1:

A train moves at a speed of 54km/h for one-quarter minute. Find the distance travelled by the train.

Solution:

Speed =    54km/h    =   15m/s

Time =    ¼ min = ¼ × 60  =  15s

Distance = speed (m/s)  ×  time (s)

           = 15(m/s)  ×  15(s)

            = 225m

ACCELERATION & RETARDATION

Acceleration is defined as the increasing rate of change of velocity. It is measured in m/s2.

Acceleration (a) = Increasing Velocity change ÷ Time taken

   When the velocity of a moving body increases by an equal amount in equal intervals of time, no matter how small the time intervals may be, it is said to move with uniform acceleration.

Retardation is defined as the decreasing rate of change of velocity. It is measured in m/s2.It is also known as deceleration or negative acceleration

Retardation (ar) = Decreasing Velocity Change ÷ Time Taken               

EQUATION OF UNIFORMLY ACCELERATED MOTION

S = (v+u) t         …………. i                     

          2

v = u + at        ..…………   ii         

v2 = u2 + 2 aS    ……….   iii                

S = ut + ½ at2    ………..   iv            

Equations (i) to (iv) are called equations of uniformly accelerated motion and could be used to solve problems associated with uniformly accelerated motion where u- initial velocity( m/s), v  final velocity (m/s), an acceleration (m/s2), s  distance covered and t  time (m).  

                                                                               Example

A car moves from rest with an acceleration of 0.2mls2. Find its velocity when it has moved a distance of 50m.

Solution:

a = 0.2mls2 , S = 50m, u = 0m/s , v = ?

v2 = u2 + 2 as

v2 = 02 + (2×0.2×50) = 20

v = √20 m/s

GRAPHS

The motion of an object is best represented or described with graphs. These graphs are:

1. Distance- time
2. Displacement  time
3. Velocity  time

Velocity Time Graph

The velocity-time graph is more useful than any of the two graphs described above because it gives more useful information concerning the motion of objects. The following information can be obtained from the graphs (i) acceleration (ii) retardation  (iii) distance   (iv) average speed.

The motion of objects can form shapes such as square, triangle, trapezium, rectangle or a combination of two or more shapes. Thus, the sum of the areas of the shapes formed corresponds to the distance moved, covered or travelled by the objects.