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**Looking at position, velocity, and acceleration from the integral.**

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

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

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

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

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**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?

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**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 . . .

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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]

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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]

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**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.

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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.

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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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Graphical Analysis of Linear Motion. A car travels along a road at a constant velocity of 10. m/s time (s) position (m) 0 0 1 10 2 20 3 30.

Graphical Analysis of Linear Motion. A car travels along a road at a constant velocity of 10. m/s time (s) position (m) 0 0 1 10 2 20 3 30.

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