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Displacement with constant acceleration. How far, how fast?. Review of v avg. We have seen a way to calculate v avg already: v avg = Δ x / t Let’s look at the Old School way to find an average…. Finding an average…. If you wanted to find the average of these numbers: 5,3,7 and 5
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Displacement with constant acceleration How far, how fast?
Review of vavg • We have seen a way to calculate vavg already: vavg= Δx / t • Let’s look at the Old School way to find an average….
Finding an average… • If you wanted to find the average of these numbers: 5,3,7 and 5 You would just add them up and divide by 4 Mmmk.
Finding an average… • You can do the same thing with velocities • Suppose a car accelerates from 0m/s for 30 sec at 1m/s2. That’s gonna take forever to do!
Finding an average…. • OR… There’s a much easier way: • If acceleration is constant (it always will be for us.) average the first and last velocities and you get the same answer. Oh, good!
Two equations • We now have two ways to find vavg : • Now let’s put them together… Uhhhh…
One equation • 1st: …
One equation • 1st: • Now, substitute in • 2nd: …
One equation • 1st: • Now, substitute in • 2nd: • New Equation: Ok, got it!
Example • A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find the distance that the car travels during braking.
Example • A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find the distance that the car travels during braking. • Givens: vi=42 m/s t= 5.5 s vf=0 m/s Δx= ?
Example • A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find the distance that the car travels during braking. • Givens: vi=42 m/s t= 5.5 s vf=0 m/s Δx= ? • Formula:
Example • A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find the distance that the car travels during braking. • Givens: vi=42 m/s t= 5.5 s vf=0 m/s Δx= ? • Formula:
Practice • For classwork, complete Practice C, Pg. 53