1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example...

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1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 - braking. Falling Objects. Example 3 – falling from tower Example 4 – falling from tower. Example 5 – throwing ball up.

Transcript of 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example...

Page 1: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

1-D Constant Acceleration

• Review • Why constant acceleration?• Constant acceleration equations.• Example 1 - runway.• Problem solving strategy.• Example 2 - braking.• Falling Objects.• Example 3 – falling from tower• Example 4 – falling from tower.• Example 5 – throwing ball up.

Page 2: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

Review

• Position

• Velocity

– vavg = (x2 –x1)/Δt = Δx/Δt

– vinst = limt->0(Δx/Δt ) = dx/dt

• Acceleration

– aavg = (v2 –v1)/Δt = Δv/Δt

– ainst = limt->0(Δv/Δt ) = dv/dt = d2x/dt2

• Signs (+/-) of x, v, and a must agree!

Page 3: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

Position, Velocity, and Acceleration

• Car entering highway, then exiting

• Elevator going to upper floors, returning

• Car backing out of driveway

• Ball dropping

• Ball thrown up

• Must be sign consistent between x, v, a!

• Up positive, down negative (down positive)

Page 4: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

Why constant acceleration?

• Position -> velocity -> acceleration – why not go further?– Constant acceleration problems common, changing

acceleration problems not!

– Newton’s 2nd Law involves acceleration.

• F=ma

– We deal with changing acceleration if we need to!

Page 5: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

Constant acceleration equations

• Acceleration constant

• Velocity from acceleration

– v = vo + at

• Position from acceleration

– x = vt (no! v is changing!)– x = (v + vo) / 2 * t

– x = (at + vo + vo) / 2 * t

– x = at2/2 + 2vot/2

– x = ½ at2 + vot + xo

a

t

t

v

vo

t

x

xo

This is supposed to be parabola!

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Constant acceleration equations

• Simplify for a=0 , v= 0

• (+/-) consistency

• Unit calculations

• We will provide on exam

Page 7: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

Power rule of calculus

Page 8: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

Example 1 - Runway

• Example 2.7 runway design– Solve with time as intermediate step

• Find distance at takeoff velocity

• Find takeoff velocity at distance

– Solve without time as intermediate step

Page 9: 1-D Constant Acceleration Review Why constant acceleration? Constant acceleration equations. Example 1 - runway. Problem solving strategy. Example 2 -

Solve without finding time• Given

• Solve

• Multiply by 2a

• Solve runway problem again

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Constant acceleration equations

(Note special case a = 0)

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Problem solving strategy

• Read problem well.• Decide what object you’re going to study.• Draw diagram, axes, positive/negative.• Decide principles that apply.• Write “knowns” and “unknowns”.• Decide relevant equations (validity?)

– OK to “just write equations, and see what happens” IF THEY ARE RELEVANT!

• What is “the trick” to the problem?– Translating a qualitative question into numbers, criterion, or equation.

• Do calculation (round result)• Does it make sense?• Do units check?

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Example 2 – Braking

• Example 2.9 braking distanceEstimate minimum stopping distance of car travelling at 50 km/h (14 m/s) if maximum acceleration is -6 m/s2 and reaction time is 0.5 s

– What are principles?– What are equations? – Write down what’s known– Solve reaction time distance– Solve braking time– Solve braking time distance