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

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Presentation on theme: "Straight Line Motion Looking at position, velocity, and acceleration from the integral."— Presentation transcript:

1 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) = t 2 – 7t +10 ft/sec. Find the displacement and distance on the interval [1, 7]

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10 4)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.


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