Question

An object is moving so that its speed after t minutes is v (t ) = 1 + 4t + 3t2 meters per minute. How far does the object travel during the 3rd minute?

Answer 1

path is the first derivative ofspeed. So we should find anintegral of the function of speed.

$$\int_{2}^3 v(t)= =\int_{2}^3 (1+4t+3t^2)=$$

$=(t+4t^2/2+3t^3/3)= (t+2t^2+t^3)|_{2}^3 =$

$=3+18+27-2-8-8= 48-18= 30 m$

Answer: Diring 3rd minute object travel on 30 meters.