Then
Since y(0) = 0, this yields C′ = 1, and so (2) becomes
Thus the parametric equations are
x = (t + 1)^2 and BC ONLYExample 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