Concepts in MechanicsThe speedomete

Concepts in Mechanics
The speedometer of a car or a bus tells us its instantaneous speed. You will learn how to find the instantaneous speed and instantaneous velocity.

Fig. 1.8: Non-uniform motion
Study Fig. 1.8. Draw straight lines joining the points A and B on the curve with the origin. What is the change in the position of the ball between the times t1 (= 1 s) and t2 (= 3 s)? What is the average speed of the ball? What is its average velocity? Remember that the direction of the velocity is in the same direction as that of the change in position.
Now take two points C and D on the curve closer to each other. Draw the straight lines OC and OD. Calculate the change in position, the average speed and the average velocity between the times t3 (= 2 s) and t4 (= 2.1 s). What is the direction of velocity in this case?
What happens to the change in position, average speed and average velocity as you bring the point D closer and closer to C? Do you notice that as D gets closer to C, the time interval t4 − t3 becomes very small? We get closer to the instant of time t3. The values of average speed and average velocity also get closer to the values of instantaneous speed and instantaneous velocity.

NOTE
The instantaneous speed of an object with non-constant speed at a point can be found from the slope of a line tangent to its path given by the curve x(t).


THE DIRECTION OF INSTANTANEOUS VELOCITY IS ALONG THE TANGENT TO THE CURVE AT THE POINT C IN THE DIRECTION OF THE CHANGE IN POSITION.



How do we describe the change in the speed and velocity of any object with time? For this, we need to introduce the concept of ACCELERATION.
Recall that the velocity of an object tells us how its displacement changes with time. In the same way, the acceleration of an object tells us how its speed or velocity CHANGES WITH TIME. Just as we defined average speed/average velocity and instantaneous speed/instantaneous velocity, we shall define AVERAGE ACCELERATION AND INSTANTANEOUS ACCELERATION.