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3-3 Velocity and Acceleration

3-3 Velocity and Acceleration. Velocity. Average Velocity Vector measurement that is the change in distance per some change in time V = Δ d / Δ t = (d 1 – d 0 ) / (t 1 – t 0 ) What is the average velocity of a car starting from rest if it travels 400.0 meters in 11.3 sec?

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3-3 Velocity and Acceleration

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  1. 3-3 Velocity and Acceleration

  2. Velocity • Average Velocity • Vector measurement that is the change in distance per some change in time • V = Δd / Δt = (d1 – d0) / (t1 – t0) • What is the average velocity of a car starting from rest if it travels 400.0 meters in 11.3 sec? • V = Δd / Δt = (d1 – d0) / (t1 – t0) • (400.0 m– 0 m) / (11.3 sec – 0 sec) • 35.4 m/s

  3. Velocity Suppose it takes a sprinter 9.87 seconds to run a 100.0 m dash. At half way (50.0 meters), the sprinter’s time is at 5.12 sec, determine the average velocity of the sprinter in the last 50.0 meters.

  4. Avg. Velocity motion diagrams • You can use arrows to show the proportional relationship between the avg. vel. Vector and displacement • o 0 0 0 0 • When displacement is larger over some unit of time, so is velocity • Is velocity positive or negative? • Depends on the origin

  5. Rearrange the equation by multiplying both sides by Δt • Δd = vΔt • Substitute d1 – d0 for Δd in first equation • d1 – d0 = vΔt • Add d0 to both sides • d1 = d0 + vΔt

  6. d1 = d0 + vΔt • Over some time interval (Δt), the avg. velocity of a moving object results in a change in position equal to vΔt

  7. Acceleration • An object in motion whose velocity is changing is said to be accelerating • Change in velocity over a period of time can determine average acceleration • a = Δv / Δt = (vf – vi) / (tf – ti) • Unit is m/s2

  8. Acceleration • A runner has an initial pace of 5.60 m/s. In a matter of 3.00 sec, the runner has a pace of 6.70 m/s. What was the average acceleration? • a = Δv / Δt = (vf – vi) / (tf – ti) • a = (6.70 m/s – 5.60 m/s) / (3.00 sec – 0 sec)

  9. Motion diagrams to obtain Average Acceleration Finding the Avg. Accel. using motion diagrams by observing the magnitude of each velocity vector Acceleration vector is proportional to the change in average velocity vector 0 0 0 0 0 0 o ooooo When Avg. velocity is speeding up in the positive direction, Avg. Accel is positive. When Avg. velocity is slowing down in positive direction, Avg. Accel is negative

  10. Determine the direction of acceleration vi vf a = vi vf a =

  11. Sketching the Problem • A driver is going at constant speed of 25 m/s, sees a child running into the road. It takes the driver 0.40 sec to hit the brakes. The car slows at a rate of 8.5 m/s2. What is the total distance the car moves before it stops? • Two step problem • From initial speed to when brakes are applied • From the starting of the breaking to full stop

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