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
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
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, Ds is the distance the body has gone in the very short time interval Dt at the specified moment. (D is the capital Greek letter delta.) Instantaneous velocity is what a car’s speedometer indicates.
A body whose velocity is changing is accelerated. A body is accelerated when its velocity is increasing, decreasing, 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
A positive acceleration means an increase in velocity; a negative acceleration (sometimes called deceleration) means a decrease in velocity. Only constant accelerations are considered here.
The defining formula for acceleration can be rewritten to give the final velocity v of an accelerated body:
Velocity has the dimensions of distance/time. Acceleration has the dimensions of velocity/time or distance/time2. A typical acceleration unit is the meter/second2 (meter per second squared).