1. The position of a particle is given by the function: S(t) = t³ – 6t² + 9t where t is in seconds, S(t) is in meters and 0 st<5. a. Write the velocity function and find the velocity after 0.5 seconds, 2 seconds and 4 seconds.

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1. The position of a particle is given by the function: S(t) = t³ – 6t² + 9t where t is in scconds, S(t) is
in meters and 0 < t < 5.
a. Write the velocity function and find the velocity after 0.5 seconds, 2 seconds and 4 seconds.
b. Find the times when the particle is at rest. Then find the position of the particle when it is at rest and at
t=0 and t=5.
c. Draw a diagram to represent the motion of the particle. Label the times and positions of the particle and the
direction in which it is traveling.
Transcribed Image Text:1. The position of a particle is given by the function: S(t) = t³ – 6t² + 9t where t is in scconds, S(t) is in meters and 0 < t < 5. a. Write the velocity function and find the velocity after 0.5 seconds, 2 seconds and 4 seconds. b. Find the times when the particle is at rest. Then find the position of the particle when it is at rest and at t=0 and t=5. c. Draw a diagram to represent the motion of the particle. Label the times and positions of the particle and the direction in which it is traveling.
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