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Acceleration

Learn about acceleration's definition, average acceleration, acceleration as a vector, velocity-time graphs, and how to solve acceleration problems with examples and practice exercises.

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Acceleration

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  1. Acceleration

  2. Acceleration = change in velocity

  3. Changing velocity • When you change velocity- either speed or direction- you have acceleration • Remember our motion diagrams? • When magnitude of velocity changes, distance between dots changes

  4. Speed and Acceleration • When could you have acceleration but have constant speed?

  5. Acceleration is a Vector! • This means it has both magnitude and direction • Rule of thumb: if acceleration is in same direction as velocity= speeding up • If acceleration is in opposite direction of velocity= slowing down

  6. Average Acceleration • a=v/ t • Units are m/s2 • Because acceleration is a vector, the sign means direction • Remember the rule of thumb: same sign as velocity then speeding up

  7. Velocity-Time Graphs • If you graph velocity vs. time, the slope (or rise/run) would be the v/ t • So slope of a v-t graph=acceleration

  8. Meaning of v-t graphs • Flat line=constant velocity= no acceleration • the position of the line above or below the x axis has meaning • In this case, is velocity + or - and how can you tell?

  9. Position of line above/below x axis denotes + or - velocity

  10. Slope= acceleration but beware of sign of velocity!

  11. Using graphs to find acceleration • Rise/run= v/ t

  12. Problem solving • Acceleration =v/ t • Remember your problem-solving steps- it becomes very important to sketch the problem- if you sketch the velocity and acceleration vectors, it will help you determine signs • Check your units- they should easily cancel to give the correct units for your answer

  13. Example: • A race car’s velocity increases from 4.0 m/s to 36 m/s over a 4.0s time period. What is the average acceleration? • Acceleration =v/ t • a=(36.0m/s-4.0m/s) = 8.0 m/s2 4.0s

  14. Practice Problems • P. 64 #7, 8

  15. Velocity-Time Graphs and Displacement • If the slope of a v-t graph shows acceleration, how can we find the displacement? • The area under a v-t graph is the displacement for that segment

  16. Calculating area • Remember area calculations? • Area of a rectangle= • d=length * width • d= t* v • Area of a triangle= •  d=1/2 base*height • d=1/2 t * v

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