Barrons AP Calculus - David Bock

Thus the parametric equations are

BC ONLY

EXAMPLE 6

The particle in Example 5 is in motion for 1 second, 0 ≤ t ≤ 1. Find its position, velocity, speed,

and acceleration at t = 1 and the distance it traveled.

SOLUTION: In Example 5 we derived the result the parametric representation

of the particle’s position. Hence its position at t = 1 is

From P(t) we write the velocity vector:

Hence, at t = 1 the particle’s velocity is

Speed is the magnitude of the velocity vector, so after 1 second the particle’s speed is

The particle’s acceleration vector at t = 1 is

On the interval 0 ≤ t ≤ 1 the distance traveled by the particle is

BC ONLY

EXAMPLE 7

A particle P(x, y) moves along a curve so that its acceleration is given by