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# Lect_04 - x(t v(t a(t In general for 1D motion along a...

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Lecture 4 Constant acceleration in 1D x (t) v (t) a (t) In general, for 1D motion along a straight line: 0 0 ( ) t dx v x x v t dt dt = = + 0 0 ( ) t dv a v v a t dt dt = = + 0 0 0 0 ( ) ( ) t t dv a v v a t dt dt dx v x x v t dt dt = = + = = + One Dimensional Constant acceleration. 1 Basic math: 1 n n x x dx n + = + When a = constant, the equations are simple: 0 0 0 2 0 0 ( ) 1 2 t x x v at dt x x v t at = + + = + + 0 0 0 t v v a dt v v at = + = + One Dimensional Constant acceleration. From these we can derive a couple more useful equations: 2 0 0 0 1 2 v v at x x v t at = + = + + 2 2 0 2 v v a x = 0 2 v v v + = 2 0 0 0 0 0 0 1 1 1 2 ( ) 0 2 2 2 v t at x x v v v v at v v v t t + + = = = + = + = 2 0 0 0 0 0 2 2 2 0 0 0 0 2 2 0 1 2 2 2 2 v v v v v v t x x v a a a a vv v v v vv a a v v a = = + + = + =

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One Dimensional Constant acceleration. 0 v v at = + 2 2 0 2 v v a x = 0 2 v v v + = 2 0 0 1 2 x x v t at = + + A car is traveling with v 0 = 10 m/s. At t = 0, the driver puts on the brakes, which slows the car to a stop in 2 seconds. a. What is the acceleration produced by the brakes? “Translate” the problem –understand it: Draw a figure. Identify and include initial ( t = 0, v 0 = 10 m/s) and final situation ( t = 2s; car stopped) Start of braking t = 0, v 0 = 10 m/s t = 2 s , stopped v = 0 EXAMPLE: Braking Car EXAMPLE: Braking Car A car is traveling with v 0 = 10 m/s At t = 0, the driver puts on the brakes, which slows the car to a stop in 2 seconds.
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Lect_04 - x(t v(t a(t In general for 1D motion along a...

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