Question

find the distance covered by the object during this time by taking the limit of the associated Reiman sum write the exact answer do not round

Answer 1

Answer

Distance = 26.4 m

Explanation

The given velocity function of the moving object is v(t) = 10 - 0.4t² m/s from t = 0 s to t = 3 s.

Distance, S is

$S=\int ^3_0v\text{ dt}$$\begin{gathered} S=\int ^3_0(10-0.4t^2)\differentialDt t \\ =\lbrack10t-\frac{0.4t^2}{3}+c\rbrack^3_0 \\ =\lbrack10\times3-\frac{0.4\times3^3}{3}+c\rbrack-\lbrack10\times0-\frac{0.4\times0^3}{3}+c\rbrack \\ =\lbrack30-\frac{10.8}{3}+c\rbrack-\lbrack0-0+c\rbrack \\ =30-3.6+c-c \\ =26.4\text{ m} \end{gathered}$