5.5 optimization

7
Rectilinea r Motion

Transcript of 5.5 optimization

Page 1: 5.5 optimization

Rectilinear Motion

Page 2: 5.5 optimization

Velocity and Speed

Velocity:

Speed:

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Acceleration

OR

Speeding up and Slowing down

v(t) > 0 and a(t) > 0v(t) < 0 and a(t) < 0 Particle is speeding up

v(t) > 0 and a(t) < 0v(t) < 0 and a(t) > 0

Particle is slowing down

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Let’s see how to calculate this !!

Let be the position function of a particle moving along an s-axis, where is is in meters and t is in seconds. Find the velocity, speed and acceleration functions, and show the graphs of position, velocity, speed and acceleration versus time.

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Analyzing position versus time curvePosition versus Time

CurveCharacteristics of the curve at t = to

Behavior of the Particle at t = to

• s(to) > 0• Positive slope• Concave down

• Particle is a the positive side of the origin• Particle is moving in the positive dir.• Velocity is decreasing• Particle is slowing down

• s(to) > 0• Negative slope• Concave down

• Particle is a the positive side of the origin• Particle is moving in the negative dir.• Velocity is decreasing• Particle is speeding up

• s(to) < 0• Negative slope• Concave up

• Particle is a the negative side of the origin• Particle is moving in the negative dir.• Velocity is increasing• Particle is slowing down

• s(to) > 0• Zero slope• Concave down

• Particle is a the positive side of the origin• Particle is momentarily stopped• Velocity is decreasing

to

to

to

to

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Practice Time !!!Suppose that the position function of a particle moving on a coordinate line is given by .Analyze the motion of the particle for t > 0. Summarize the information schematically.

v(t)

a(t)

0 2 7/2 5

0 2 7/2 5

+ + + + + + + + + 0 - - - - - - - - - - - - - - - - - - - -0 + + + + + + +

- - - - - -- - - - - - - - - - - - - - - - - -0 + + + + + + + + + + + + + + +

Slowing down Speeding up Slowing down Speeding up

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Not Done Yet !!!

0 3 28 41.5 55 s(t)

t = 0 t = 2

t = 7/2t = 5

Slowing down

Speeding upSlowing down

Speeding up