A body moves along a straight line so that its velocity vat time tis given by v= 4t^3 + 3t^2 +5. The distance the body covers from t= 0 to t= 2 equals

Question

A body moves along a straight line so that its velocity vat time tis given by v= 4t³ + 3t² +5. The distance the body covers from t= 0 to t= 2 equals

(A) 34

(B) 55

(C) 24

(D) 44

(E) none of these

Answer 1

Because v(t) > 0 on this time interval, displacement = total distance traveled = ∫₀²v(t)dt

dist = ∫₀² (4t³ + 3t² + 5)dt = t⁴ + t³ + 5t ]₀² = 34