Phys2A_F07_Lecture_07

Phys2A_F07_Lecture_07 - Motion with Constant Acceleration...

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W. P. Beyermann Fall 2007 1 Motion with Constant Acceleration Assume s i = 0; and v is and a s > 0 Kinematics

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W. P. Beyermann Fall 2007 2 f i s i f t t v s s and between curve velocity under the area + = 2 2 1 ) ( t a t v s s s is i f Δ + Δ + = t a v v t v v t v a s is fs is fs s s Δ + = Δ = Δ Δ = (1) (2)
W. P. Beyermann Fall 2007 3 s a t Δ t a v v s is fs Δ + = 2 2 1 ) ( t a t v s s s is i f Δ + Δ + = ) ( 2 2 2 i f s is fs s s a v v + = t v v s s fs is i f Δ + + = ) ( 2 1 Contains Equations ( s i and v is are known) XXX XX X X Kinematic Equations for Motion with Constant Acceleration f s fs v

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W. P. Beyermann Fall 2007 4 Bob is driving the getaway car after a bank robbery. He’s going 50 m/s when his headlights suddenly reveal a nail strip that the cops have placed across the road 150 m in front of him. If Bob can stop before hitting the strip, he can turn around and escape. If he hits the nail strip, his tires will go flat, and he will be apprehended. Bob’s reaction time for applying the brakes is 0.6 s, and his car’s maximum deceleration is 10 m/s 2 . Does Bob go to jail? • Represent Bob’s car as a particle. • Represent the nail strip as a line across the road. • Assume the tires go flat if the car reaches the nail strip. • The deceleration of Bob’s car instantly goes from zero to its new constant value, 0.6 s after Bob sees the nail strip. • Because the acceleration changes from one constant value to another at a point in time, the problem can be separated into 2 sequential parts. Model • The problem starts the instant Bob sees the nail strip. Example: Bob’s Bank Robbery
W. P. Beyermann Fall 2007 5 Pictorial Representation 0 x Bob sees nail strip Applies brakes Comes to a stop Nail strip t 0 x 0B v 0B t 1 x 1B v 1B t 2 x 2B v 2B x N 0 0 = a G 1 a G Known t 0 = x 0B = 0 a 0 = 0 v 0B = v 1B = 50 m/s t 1 = 0.6 s v 2B = 0 x N = 150 m a 1 = 10 m/s 2 Find x 2B and x 1B

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W. P. Beyermann Fall 2007 6 Physical Representation – Motion Diagram Sees nail strip Applies brakes Comes to a stop 0 0 = a G 1 a G Part 1 of motion Part 2 of motion
W. P. Beyermann Fall 2007 7 2 0 1 0 2 1 1 0 0 1 ) ( t t a t v x x B B B + + = m 30 s 6 . 0 m/s 50 ) s 6 . 0 ( 0 s 6 . 0 m/s 50 0 2 2 1 1 = × = × + × + = B x ) ( 2 ) ( ) ( 1 2 1 2 1 2 2 0 B B B B x x a v v + = = ± ² ³ 2 1 1 2 1 ) ( ) ( 2 B B B v x x a = 1 2 1 1 2 2 ) ( a v x x B B B = m 155 ) m/s 10 ( 2 ) m/s 50 ( m 30 2 2 2 = = B x 1 2 1 1 2 2 ) ( a v x x B B B = Find N B x x > 2 He is going to jail.

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Phys2A_F07_Lecture_07 - Motion with Constant Acceleration...

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