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Sect. 3-A Position , Velocity, and Acceleration

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## Sect. 3-A Position , Velocity, and Acceleration

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**Position function -**gives the location of an object at time t, usually s(t), x(t) or y(t) Velocity - The rate of change( derivative) of position, usually v(t) Acceleration - The rate of change ( derivative) of velocity usually a(t) Average velocity -**1) If**find v(t) and a(t).**2) The position of a particle moving along the x - axis at**time t is given by . Find the particles velocity and acceleration at t = 5. Velocity Acceleration**Speed – The absolute value of velocity otherwise known as**the magnitude of velocity**Velocity**Positive - the particle is moving to the right Negative - the particle is moving to the left Zero - the particle has momentarily stopped or is changing direction ( must have a sign change)**3) Find where the object changes direction if**Find where v(t) = 0**Acceleration and Velocity**• If the sign of acceleration is the same as velocity, the speed of the particle is ______________ (the two are working together) • If the sign of the acceleration is opposite that of velocity, the speed of the particle is _________________ (the two are working against each other)**4) Given the same position function as #3**find the interval during which the particle is slowing down.**5) Given find the**interval during which the particle is speeding up.**Distance vs. Displacement**• Displacement- change in position ( final position minus original position) • Distance- the total distance travelled by an object in the time interval even if duplicated**Consider two**intervals 6) Find the DISTANCE traveled by the particle whose position is given by on the interval (0,4). Distance NOT displacement!!**7) If**• find the DISTANCE traveled by the particle on the interval (2,4). • Find the DISPLACEMENT on the interval (1,5)**The graph shows the position function of a radio controlled**car a) Was the car going faster at B or at C? b) When was the car stopped? c) At which point was the car’s velocity the greatest? d) At which point was the car’s speed decreasing?**Homework**PVA Worksheet and worksheet 3-A