The velocity function (in meters per second) is given for a particle moving along a line.

Question

The velocity function (in meters per second) is given for a particle moving along a line.

v(t) = 5t − 9,    0 ≤ t ≤ 3

(a) Find the displacement.

(b) Find the distance traveled by the particle during the given time interval.

Answer 1

(a) s= ∫₀³(5t - 9)dt = (5t²/2- 9t)₀³ = 45/2 - 27 = - 4.5 m

(b) Distance d = ∫₀³I5t - 9Idt = ∫₀^9/5(9 - 5t)dt + ∫_9/5³(5t - 9)dt = (9t - 5t²/2)₀^9/5 + (5t²/2 - 9t)_9/5³ = 81/5 - 81/10 +

45/2 - 27 - 81/10 + 81/5 = 81/5 - 9/2 = 16.2 - 4.5 = 11.7 m