Solution Found!
The position of a particle moving along the x-axis is given by x(t) = t 3 9t2 + 24t
Chapter 17, Problem 6(choose chapter or problem)
The position of a particle moving along the x-axis is given by x(t) = t 3 9t2 + 24t metres where t is in seconds, t > 0. a Draw sign diagrams for the particles velocity and acceleration functions. b Find the position of the particle at the times when it reverses direction, and hence draw a motion diagram for the particle. c At what times is the particles: i speed decreasing ii velocity decreasing? d Find the total distance travelled by the particle in the first 5 seconds of motion
Questions & Answers
QUESTION:
The position of a particle moving along the x-axis is given by x(t) = t 3 9t2 + 24t metres where t is in seconds, t > 0. a Draw sign diagrams for the particles velocity and acceleration functions. b Find the position of the particle at the times when it reverses direction, and hence draw a motion diagram for the particle. c At what times is the particles: i speed decreasing ii velocity decreasing? d Find the total distance travelled by the particle in the first 5 seconds of motion
ANSWER:Step 1 of 7
The position of the particle (displacement function) is modelled as,
(a)
The velocity and acceleration can be obtained as,
Differentiate the displacement function to obtain the velocity,
Differentiate the velocity function to obtain the acceleration,
