Displacement with constant acceleration
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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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Review of v avg
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
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 average1
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 average2
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
Two equations

  • We now have two ways to find vavg :

  • Now let’s put them together…

Uhhhh…


One equation
One equation

  • 1st:


One equation1
One equation

  • 1st:

  • Now, substitute in

  • 2nd:


One equation2
One equation

  • 1st:

  • Now, substitute in

  • 2nd:

  • New Equation:

Ok, got it!


Example
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.


Example1
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= ?


Example2
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:


Example3
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
Practice

  • For classwork, complete Practice C, Pg. 53


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