Rectilinear Motion

Velocity and Speed

Velocity:

Speed:

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

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.

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

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

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