Total Distance & Particle Motion

1. Total Distance & Particle Motion Warm – Up: Given the distance function f(t) = -2t3 + 4t2 find when the velocity is zero.

2. Warm – Up Cont: If the velocity of an object is zero, what does this mean? If the velocity is positive what does it mean? If the velocity is negative what does it mean?

3. Total Distance Travelled: 1) Miss Terry is very forgetful. On her way to go running she realized that she had forgotten her shoes and had to run back home to get them before heading to the park. Her location at a given time is given by the formula d(t) = 1/3t3 – t2 – 3t. Find the total distance she had to travel if she got to the park 6 minutes after leaving the house.

4. v(x) 2) The below graph represents the velocity of a car. Find the total distance the car traveled. 1 x r=2 1

5. Particle Motion: • If the velocity of a particle is positive then the particle is moving _______ or _______. • If the velocity of the particle is ________ then the particle is moving left or down. • To find the average velocity over a time interval, divide the change in ______ by the change in time. • If the acceleration of the particle is positive, then the ___________ is increasing. • If the acceleration of the particle is __________, then the velocity is decreasing. • In order for the particle to change direction, the ______________ must change signs.

6. Example: A particle is moving horizontally. Its distance from a fixed point at a given time is given by f(t) = -2/3t3 + 9/2t2 – 10t. At time t = 1, is the particle moving right or left?

7. Example: A particle is moving horizontally. Its distance from a fixed point at a given time is given by f(t) = -2/3t3 + 9/2t2 – 10t. Is there a time between t = 1 and t = 3 when the particle is at rest?

8. Example: A particle is moving horizontally. Its distance from a fixed point at a given time is given by f(t) = -2/3t3 + 9/2t2 – 10t. At t = 1 is the velocity increasing or decreasing?

9. Example: A particle is moving horizontally. Its distance from a fixed point at a given time is given by f(t) = -2/3t3 + 9/2t2 – 10t. Find the total distance the particle travelled over the time interval 0 ≤ t ≤ 3