Motion on a Plane
We can use calculus to understand the motion of an object in two dimensions on a flat plane. In this case we use a pair of parametric equations, x(t) and y(t) to represent the position on the plane of the object at time t. The derivatives with respect to t of these two functions give the x and y components of the velocity of the object:
) = x
) and vy
) = y
The speed, or magnitude of velocity, is given by
Note that the velocity is a vector, in that it has both a magnitude and a direction.
Similarly, the acceleration has two components:
) = x
) and ay
) = y'
and its magnitude is computed as