(4) Constant Acceleration in 1 Dimension

(4) Constant Acceleration in 1 Dimension - Lecture 4...

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Unformatted text preview: Lecture 4 Constant acceleration in 1D x(t) v(t) a(t) I n general, for 1D motion along a straight line: ( ) t dx v x x v t dt dt = = + & ( ) t dv a v v a t dt dt = = + & ( ) ( ) t t dv a v v a t dt dt dx v x x v t dt dt = = + = = + & & One Dimensional Constant acceleration. 1 Basic mat h: 1 n n x x dx n + = + When a = constant, the equations are simple: 2 ( ) 1 2 t x x v at dt x x v t at = + + = + + t v v a dt v v at = + = + One Dimensional Constant acceleration. From these we can derive a couple more useful equations: 2 1 2 v v at x x v t at = + = + + 2 2 2 v v a x- = 2 v v v + = 2 1 1 1 2 ( ) 2 2 2 v t at x x v v v v at v v v t t +- + = = = + = +- =- 2 2 2 2 2 2 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--- =- = +- +- = +- = One Dimensional Constant acceleration. v v at = + 2 2 2 v v a x- = 2 v v v + = 2 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. I dentify and include initial (t = 0, v = 10 m/ s) and final situation (t = 2s; car stopped) Start of braking t = 0, v = 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 dr iver puts on the brakes, which slows the car to a stop in 2 seconds....
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(4) Constant Acceleration in 1 Dimension - Lecture 4...

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