position, velocity , and acceleration

POSITION, VELOCITY, AND ACCELERATION

Review- 3-C

Position:

Velocity:

Acceleration:

x(t)

v(t) x (t)

a(t) v (t) x (t)

)()(dtdxtxtvspeed

Acceleration vs Velocity

• If the signs are the same, then the particle’s speed is increasing

• If the signs are opposite, then the particle’s speed is decreasing

• If the velocity is zero and acceleration is not zero, then the particle is momentarily stopped and changing directions.

Velocity

• If v(t) > 0 then the particle is moving to the right• If v(t) < 0 then the particle is moving to the left• If v(t) = 0 then the particle has momentarily stopped

or is changing directions

1) The position of a particle moving along the x - axis at time t is given by

for 0≤ t ≤ 20 a) Determine when the particle is moving to the left?

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1) The position of a particle moving along the x - axis at time t is given by

for 0≤ t ≤ 20 b) Determine when the particle changes direction and

find its position.

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1) The position of a particle moving along the x - axis at time t is given by

for 0≤ t ≤ 20 c) Determine when the particle is speeding up?

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1) The position of a particle moving along the x - axis at time t is given by

for 0≤ t ≤ 20 d) find the total distance travelled

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2) An object is moving along the x-axis according to

for t ≥ 0 find all intervals during which the object is moving in a positive direction.

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3) An object is moving along the x-axisaccording to

for 0≤ t ≤ 6 find the intervals during which the object is speeding up.

3sin)( ttx

4) If find the total distance traveled by the particle on the interval (0,4).

24 8)( tttx

HOME WORKWorksheet 3-B position, velocity and acceleration.