1. Looking at position, velocity, and acceleration from the integral.
Straight Line Motion
Looking at position, velocity, and acceleration from the integral.

2. What does s(t), v(t), and a(t) mean? How are they connected?

3. 1) a(t) = 4t – 6 and the initial velocity is 3, find v(t).

4. 2) a(t) = sin t + 2t and the initial velocity is 5, find v(t).

5. Displacement and Distance
80 miles to the right then turn around …
Go 30 miles back
Displacement = 80 – 30 or 50 miles
Distance = or 110 miles
Can displacement equal distance? How?

6. Displacement and Distance
80 miles to the right then turn around …
Go 30 miles back
Given a particle moving on a straight line with velocity v(t) between time t = a and time t = b then . . .

7. 3) A particle is moving along a straight line with velocity v(t) = t2 – 7t +10 ft/sec. Find the displacement and distance on the interval [1, 7]

8. 3) A particle is moving along a straight line with velocity v(t) = t2 – 7t +10 ft/sec. Find the displacement and distance on the interval [1, 7]

10. Given an object moving in a straight line with
v(0) = -18, t = 0 to t =16.
Find v(t) and the displacement and distance of the object.

11. 5) A subway train accelerates as it leaves one station, then decelerates as it comes into the next station. The following chart measures the velocity v given in miles per hour.
a) Find the distance the train travels every 5 second interval.

12. 5) A subway train accelerates as it leaves one station, then decelerates as it comes into the next station. The following chart measures the velocity v given in miles per hour.
b) Find the total distance between subway stops.