A particle moves along a line so that its velocity at time t is v(t) = 3t^2-12 (

Question

A particle moves along a line so that its velocity at time t is v(t) = 3t^2-12 (measured in meters per second).

(a) Find the displacement of the particle during the time period 1 ? t ? 3.

(b) Find the distance traveled during this time period.

Explanation / Answer

a) S = int [ v(t) ] dt = t^3 - 12t put limits from 1 to 3 = [3^3 - 12*3 - 1 + 12] = 2 m b) D = int [ |v(t)| dt ] = int [ |3t^2 - 12| dt ] 3t^2 - 12 = 0 or t = 2 |3t^2 - 12| = +(3t^2 - 12) for t >2 = -(3t^2 - 12) for t < 2 So, D = int [ |v(t)| dt ] = int [ |3t^2 - 12| dt ] = int from 1 to 2 [ -(3t^2 - 12) ]dt + int from 2 to 3 [(3t^2 - 12)dt] = [-t^3 + 12t ] from 1 to 2 + [t^3 - 12t ] from 2 to 3 = [-2^3 + 12*2 + 1 - 12] + [3^3 - 12*3 - 2^3 + 12*2] = 12 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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