Velocity and Acceleration

1. Velocity and Acceleration in Linear Motion
   For a point moving along a straight line, if the position of the point at time is given by , then:
1. The velocity at time is the rate of change of position with respect to time:
2. The acceleration at time is the rate of change of velocity with respect to time:


2. Velocity and Acceleration in Plane Motion
   For a point moving in a coordinate plane, if the position of the point at time is given by and , then:
1. The velocity at time is given by the vector: 
   or 
2. The acceleration at time is given by the vector:
   or )

Additional Notes:

1. The magnitude of velocity (speed) is:
   
2. The magnitude of acceleration is: