Page 35 - mechanics

Chapter – 6 Kinematics of a Particle

The average velocity vav of a particle is defined as the
particle’s displacement x divided by the time interval t

during which that displacement occurs

vav = x / t (6.2)

The average velocity of a particle moving in one dimension can

be positive or negative, depending on the sign of the
displacement. (The time interval t is always positive.)

We can interpret average velocity geometrically by drawing
a straight line between any two points on the position–time
graph in Figure 11.1.b. This line forms the hypotenuse of a

right triangle of height x and base t. The slope of this line is

the ratio x/t, which is what we have defined as average

velocity. For example, the line between positions A and B in

Figure 11.1.b has a slope equal to the average velocity of the
car between those two times, (52 m – 30 m)/(10s - 0) = 2.2 m/s.

In everyday usage, the terms speed and velocity are

interchangeable but, we should distinguish between them.

The average speed of a particle, a scalar quantity, is defined

as the total distance traveled divided by the total time interval
required to travel that distance

Average speed = total distance / total time (6.3)

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