Motion with time dependent accelerationGiven an object which starts from position x=0 and moves along a straight line with position given by find: Solution: a. The velocity is given by the derivative of the position.
b. The acceleration is given by the derivative of the velocity.
c. The average velocity must be calculated from the displacement divided by the time.
The average velocity for the first 3 seconds of motion is given by
so the average velocity is 25 m/s. You can check to see that the constant acceleration expression for average velocity gives the erroneous value 22.5 m/s. d. Motion graphs. Motion equations as polynomials in time.

Index Polynomial derivatives  
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