5.8 rectilinear motion
TRANSCRIPT
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Rectilinear Motion
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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