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CHAPTER 2

MOTION

Velocity

The velocity of a body is a vector quantity that describes both how fast it is moving and the direction in which it is headed.

In the case of a body traveling in a straight line, its velocity is simply the rate at which it covers distance. The average velocity ¯v of such a body when it covers the distance s in the time t is

v=s/t

Average velocity =distance/time

The average velocity of a body during the time t does not completely describe its motion, however, because during the time t, it may sometimes have gone faster than v and sometimes slower. The velocity of a body at any given moment is called its instantaneous velocity and is given by

Here, s is the distance the body has gone in the very short time interval t at the specified moment. ( is the capital Greek letter delta.) Instantaneous velocity is what a car’s speedometer indicates.

When the instantaneous velocity of a body does not change, it is moving at constant velocity. For the case of constant velocity, the basic formula is

s = vt

Distance = (constant velocity)(time)

Solved Problem 2.1 The velocity of sound in air at sea level is about 343 m/s. If a person hears a clap of thunder 3.00 s after seeing a lightning flash, how far away was the lightning?

Solution. The velocity of light is so great compared with the velocity of sound that the time needed for the light of the flash to reach the person can be neglected. Hence

s = vt = (343 m/s)(3.00 s) = 1029 m = 1.03 km

Acceleration

A body whose velocity is changing is accelerated. A body is accelerated when its velocity is increasing, de-creasing, or changing its direction.

The acceleration of a body is the rate at which its velocity is changing. If a body moving in a straight line has a velocity of v₀ at the start of a certain time interval t and of v at the end, its acceleration is