Question

The equation of motion for a particle moving along the y-axis is given as y(t) = 3t2 - 6t + 2 for t2 0.
Part A: Find the velocity and acceleration functions. (10 points)
Part B: Describe where the particle changes direction and the intervals where the particle speeds up or slows down. (20
points)

Answer 1

Part A

• The velocity = 6t - 6

• Acceleration = 6

Part A:

The velocity function of the particle,

$V(t) = y^I(t) = 6t - 6$  (By diffentiating y with respect to t)

Acceleration function of the particle

$a(t) = y^II (t) = 6$

Part B:

The particle is stationary when its velocity is equal to zero

$V(t) = 0$ ---->

$6t - 6 = 0\\\\6t = 6 \\\\t = 1$

So the particle is moving in the positive direction, the particle speeds up in the interval (1, ∞) and slows down in the interval (0, 1)

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