A particle moves along a straight line and its position attime t is given by s(t

Question

A particle moves along a straight line and its position attime t is given by s(t)=2t^3-27t^2+84t   wheres is measured in feet and t in seconds.
Theparticle stops moving (i.e. is in a rest) twice, once when t=A andagain when t=B where A<B. A= B=
Finally,what is the TOTAL distance the particle travels between time 0and time 18?
Theparticle stops moving (i.e. is in a rest) twice, once when t=A andagain when t=B where A<B. A= B=
Finally,what is the TOTAL distance the particle travels between time 0and time 18?

Explanation / Answer

Take the derivative of the equation of the position function to getthe equation for the velocity function. You get: 6t^2 - 54t + 84 Use the quadratic formula or factor. The zeroes are at x = 2, 7 A = 2 B = 7 To find the distance traveled, you can plug the values back intothe displacement formula. At 2, it has gone 76 feet. At 7, it has gone to -49 feet, but since this question asks for thetotal distance (a scalar), you add the difference. Therefore, ithas traveled 125 feet in the 2nd segment, for a total of 201feet. At 18 feet, it has gone 4428 feet. Again, since the second pointwas negative, you add the difference. Therefore, it has traveled 4477 feet in the 3rd segment, for atotal of 4678 feet.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.