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Linear Motion Equations

Linear Motion Equations. By: Nahdir Austin . Acceleration (p 48-49). Acceleration: the rate of change of velocity with respect to time a avg = Δ v/ Δ t = (v f –v i )/( t f -t i ) Notice how this form looks similar to that of velocity ( Δ x/ Δ t)

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Linear Motion Equations

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  1. Linear Motion Equations By: Nahdir Austin

  2. Acceleration (p 48-49) • Acceleration:the rate of change of velocity with respect to time • aavg = Δv/Δt = (vf –vi)/(tf-ti) • Notice how this form looks similar to that of velocity (Δx/Δt) • Just as the slope of x vs t is velocity, the slope of v vs tis acceleration

  3. Quick math questions • A car can accelerate at a rate of 2m/s2. How long will it take for the car to reach a speed of 30 m/s? • What is the rate of acceleration for a car that slows from 30 m/s to a stop in three seconds?

  4. Variables of linear motion • d = displacement (Δx) • t = time of travel (Δt) • a = rate of constant acceleration • vi = initial velocity • vf = final velocity

  5. Definitions of linear motion • vavg= Δx/Δt • aavg= Δv/Δt

  6. Key Steps in Problem Solving • Identify what you are looking for • Identify what you know (state your variables) • Identify the equation(s) you need from the variables you have (and don’t have) • Rearrange equations to solve for the unknown • Fix any unit issues • Plug and chug • Check your units

  7. Practice # 1 • A car travelling at 10.0 m/s accelerates at a rate of 2.5 m/s2to a final velocity of 20. m/s. How long does it take for this to occur?

  8. Practice # 2 • A plane must reach a speed of 100 m/s at take off. If it takes 10 seconds to get down the runway, how long does the runway have to be?

  9. Practice #3 • Upon lift off, a rocket ship accelerates at a rate of 1 m/s2. How fast is it travelling when it reaches a height of 10,000 m?

  10. Theory behind the lab • We know: d = vit + ½ a t2 • If you drop something, vi = 0, so the equation reduces to: d = ½ at2 • If you rearrange with a on the left you get a = 2d/t2 • This lets you find the acceleration of an object due to gravity!! • You can also determine the slope of a graph of v vs. t to get a. We will do this too.

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