Average velocity and Average speed

Speed:

(i) The rate of change of distance is known as speed

(iii) Speed is a scalar quantity

Velocity  :

(i) The rate of change of displacement is known as velocity

(iii) Unit of velocity is m/s

(iv) Dimensional formula of velocity is 

(v) Velocity is a vector quantity

(vi) Both speed and velocity have same units and dimensions

Average speed:

(i) Average speed is defined as the ratio of the total distance travelled by the object of the total time taken

Instantaneous speed:

(i)  The speed of an object at a given instant of time is called its instantaneous speed.

(ii) Instantaneous speed of an object at an instant of time is defined as the limit of the average speed at the time interval Δt at the given instant of time becomes infinitesimally small.

Average velocity:

(i) The ratio of total displacement to the total time interval in which the displacement occurs is called average velocity

Example problem 1:

A man walks on a straight road from his home to a market 2.5Km away with a speed of 5Kmh^-1 .Finding the market closed, he instantly turns and walks back home with a speed of 7.5 Kmh^-1 What is the (a) magnitude of average velocity and (b) average speed of the man over the time interval 0 to 50 minutes?

Example problem 2:

A motorist drives north for 30 min at 85 Km/h and then stops for 15min. He continues travelling north and covers 130km in 2 hours. What is his total displacement and average velocity?

 Example Problem:

A car travels the first third of a distance with a speed of 10kmph, the second third at 20kmph and the last third at 60kmph. What is its mean speed over the entire distance?