Velocity and Acceleration
When the position of a point moving on a straight line is given by , the velocity and acceleration of point at time are expressed as:
The absolute value of velocity, , is called the speed of point at time , and is called the magnitude of acceleration.
The sign of velocity indicates the direction of motion of point . If , the function is increasing, meaning point is moving in the positive direction. If , the function is decreasing, so point is moving in the negative direction. When , the motion either stops or changes direction.
Rate of Change with Respect to Time
When a physical object has a length , area , or volume at time , and after a time interval these quantities change by , , and respectively, the rate of change of length, area, and volume at time are given as:
