lecture 4

# lecture 4 - Lecture 4 Motion with constant acceleration...

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1 Lecture 4 Motion with constant acceleration Free Fall

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2 Motion With Constant Acceleration Consider an object with an acceleration a . What is the object’s velocity as a function of time? dt dv a = This is a differential equation. Its solution is the function v(t). The first time derivative of this function is the object’s acceleration. Rearrange the above expression: = = dt a v dt a dv
3 If a is constant then C at dt a dt a v + = = = C is the integration constant and represents the velocity of the object when t = 0 (initial velocity). at v v + = 0 Since dt dx v = The position of the object can be determined; when a = constant: 2 0 0 2 1 at t v x x + + = Where x 0 is the position of the object when t = 0.

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4 The results at v v at t v x x + = + + = 0 2 0 0 2 1 x a v v + = 2 2 0 2 Can be combined to give
5 Example: At the instant a traffic light turns green, an automobile starts with a constant acceleration of 2.2 m/s 2 . At the same instant a truck, traveling with a constant speed

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lecture 4 - Lecture 4 Motion with constant acceleration...

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