Acceleration

Now, that’s acceleration!

rate of change in velocity acceleration, a = ____________________________ a vector (has mag. and dir.) =______________________________ average a = where Δv = Any time that _____________ changes, there is___________________. And because: velocity = + speed direction, changing either _____________ or ______________ or _________ results in acceleration. In this section, we only consider changes in __________ . The _________ speed changes, the _________ the a.

PhysRT, last page:

rate of change in velocity acceleration, a = ____________________________ a vector (has mag. and dir.) =______________________________ average a = where Δv = Δv/t vf - vi Any time that _____________ changes, there is___________________. And because: velocity = + velocity acceleration speed direction, changing either _____________ or ______________ or _________ results in acceleration. In this section, we only consider changes in __________ . The _________ speed changes, the _________ the a. speed direction both speed faster more

Ex: Mr. Siudy accelerates his jet skis from a speed of 5.0 m/s to a speed of 17 m/s in 3.0 s. Find the magnitude of her acceleration. a = Δv/t vi = 5.0 m/s = (vf – vi)/t vf = 17 m/s = (17 m/s – 5.0 m/s) 3.0 s t = 3.0 s a = ? = 12 m/s 3.0 s = 4 m/s s = 4 m/s2

SI units for a: m/s = s m/s2  derived other units: mph , s cm , s2 km/h s Using brackets [ ] for units: [a] = [speed] [time] = [distance]/[time] [time] = [distance] [time]2 4 m/s of speed _________ gained each From last problem: a = 4 m/s2 = 4 m/s s second

Because a = _________ , the ________________ of a is the same as the __________________ of the ________________in v: Dv = vf - vi. direction Dv/t direction change Ex 1: An object moving to the right accelerates to a faster speed. vi vf Dv = vf – vi vf = vf + (-vi) Dv -vi to the right Since Dv ____ 0 (which is _________________), then also the acceleration a ____ 0. > >

Ex 2: An object moving to the right is slowing down, or ________________________. decelerating vi vf Dv = vf – vi Dv vf = vf + (-vi) -vi Since Dv ____ 0, then also a ____ 0. Note that the direction of the acceleration ______________ always the same as the direction of the ___________________ . < < is NOT velocity

Ex 3: An object moving up but slowing down: vf vf Dv = vf – vi -vi = vf + (-vi) Dv vi  a is ______________ or_______________. negative downward Conclusions: If the ___________ and the________________ are in the __________ direction, then the object is _________________ ( __________________) . 2. If the ___________ and the________________ are in _______________ directions, then the object is _________________ ( __________________) . velocity acceleration same accelerating speeding up velocity acceleration opposite decelerating slowing down

_______________can be confusing, but remember: The __________________ is always from the _________________ to the _____________ points. The ________________ always has the same direction as the object's ____________________ (the _________ direction it __________________). The ___________________ has a direction given by the direction of the ____________ in the ______________ , which may or may not be the same as the direction of the ________________ . Directions displacement initial final initial final velocity displacement same is moving acceleration change velocity, Dv velocity

Ex: The _________________of the acceleration is also called the__________________________. magnitude acceleration a = 2.0 m/s2, east = + 2.0 m/s2 mag. dir. In review: scalar …is the magnitude of the… vector distance displacement speed velocity acceleration

_ In word problems, remember: 1) “starts from rest” means  vi =0 2) “comes to rest” means  vf =0 When an object is in ______________motion, it means it has a _________________velocity. In that case: __________ and ____ = _____ = _____ uniform constant a = 0 v vf vi light and sound Examples: The speed of _____________________ given in the PhysRT are ___________________. constants up/right are___________________, down/left are____________________. + _

Ex: A ball is dropped. It accelerates from rest to a speed of 29 m/s in 3.0 seconds. Finds its acceleration. “from rest”  vi = 0 a = Δv/t vf = -29 m/s (down) a = (vf – vi)/t t = 3.0 s a = -29 m/s -0 3.0 s a = ? a = -9.7 m/s2 What are the magnitude and direction of a? How much speed does the ball gain each second? 9.7 m/s2 down (neg.) 9.7 m/s

Starting from: a = Δv/t a = (vf – vi)/t at = vf – vi vf = vi + at PhysRT, last page:

Ex: What is the speed of a giraffe, initially moving at a speed of 21 m/s, that accelerates at 5.0 m/s2 for 2.0 s? vf = vi + at vi = 21 m/s = 21 m/s + 5.0 m/s2(2.0 s) a= 5.0 m/s2 = 21 m/s + 10. m/s t = 2.0 s = 31 m/s vf = ? If it remains at this final speed, how long will it take to travel 100. m? v = d/t vf = v = 31 m/s 31 = 100 / t d = 100. m t = 3.2 s

Ex: Chuck Norris accelerates from a speed of 4.0 m/s to 10. m/s in 4.0 seconds. Find his average speed during that time. v = (vi + vf) 2 not in PhyRT = (4.0 m/s + 10. m/s) 2 = 7.0 m/s How far does he travel in the 4.0 s? v = d/t d = v t = (7.0 m/s)(4.0 s) = 28 m Why can't you use vi or vf to find d?