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Unformatted text preview: Linear Motion with constant acceleration Physics 6A Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB As long as its acceleration is constant*, the motion of any object can be described by the following simple formulas: When using these formulas it is important to be clear about your variables. Especially important is where and when the position and time are zero. A couple of examples will help clarify this. *both the magnitude and direction must be constant ( 29 2 2 2 2 1 x x a 2 v v at v v at t v x x + = + = + + = (1) (2) (3) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Sample Problem #1 A 2009 Audi A4 accelerates from rest to 30 m/s in about 5.6 seconds. From that speed, it stops in a distance of 50 meters. Find the following: a) the average acceleration while it is speeding up b) the distance traveled while speeding up c) the average acceleration while braking d) the time elapsed while braking Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB By definition, average acceleration is just (change in velocity)/(change in time). Since the car sped up from 0 m/s to 30 m/s in 5.6 seconds, this is a simple calculation: 2 s m s s m 4 . 5 6 . 5 30 a ≈ = This is the answer for part a) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Sample Problem #1 A 2009 Audi A4 accelerates from rest to 30 m/s in about 5.6 seconds. From that speed, it stops in a distance of 50 meters. Find the following: a) the average acceleration while it is speeding up b) the distance traveled while speeding up c) the average acceleration while braking d) the time elapsed while braking Another way to do part a) is to use formula (2) from before: at v v + = In this case we are starting from rest, so v = 0 m/s , and our final speed is v = 30 m/s . The elapsed time is t = 5.6 s Putting these numbers into the equation we get: 30 m/s = 0 + a(5.6 s ) Solving for a gives us the answer: a ≈ 5.4 m/s 2 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Sample Problem #1 A 2009 Audi A4 accelerates from rest to 30 m/s in about 5.6 seconds. From that speed, it stops in a distance of 50 meters. Find the following: a) the average acceleration while it is speeding up b) the distance traveled while speeding up c) the average acceleration while braking d) the time elapsed while braking Now that we have the acceleration from part a), we can get the answer to b) Which of our 3 equations is appropriate here? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB ( 29 2 2 2 2 1 x x a 2 v v at v v at t v x x + = + = + + = (1) (2) (3) Sample Problem #1 A 2009 Audi A4 accelerates from rest to 30 m/s in about 5.6 seconds. From that speed, it stops in a distance of 50 meters....
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This note was uploaded on 09/09/2011 for the course PHYS 6a taught by Professor Stanek during the Spring '07 term at UCSB.
 Spring '07
 STANEK
 Physics, Acceleration

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