# lec05 - Lecture 5 P112 Office Hours Feel free to attend any...

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Lecture 5 P112 Jan 30, 2008

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Office Hours • Feel free to attend any TA office hours
Agenda for today • A few practice examples on velocity, acceleration and position • Velocity and position by integration – given the acceleration as a function of time, how do I get velocity and position? • Relative Velocity

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A quick problem: Airtrack with spring: start it by compressing the spring with cart. Take direction the cart is moving in as positive and bottom of the spring as the origin Draw the v versus t graph!
Cart with spring Which letter occurs when cart is – At highest point? – In contact with the spring? – Moving toward the spring? – Has zero acceleration?

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Cart with spring Which letter occurs when cart is – At highest point? B – In contact with the spring? D – Moving toward the spring? C – Has zero acceleration? Nowhere Draw acceleration and position
Cart with spring X(t) t a(t) t

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Velocity from acceleration Assume the acceleration as a function of time is given, how do you calculate the velocity at time t? t a(t)
Velocity from acceleration We saw that a = dv / dt In calculus you learned that dv = a dt can be integrated to obtain: In other words, the area under the a(t) graph between times 1 and 2 equals the change in velocity v 2 -v 1 a(t) t + +...+ =velocity change v 2 v 1 = dv = v 1 v 2 a x dt t 1 t 2

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lec05 - Lecture 5 P112 Office Hours Feel free to attend any...

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