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

Distance = 26.4 m

Step-by-step 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-(0.4t^2)/(3)+c\rbrack^3_0 \\ =\lbrack10*3-(0.4*3^3)/(3)+c\rbrack-\lbrack10*0-(0.4*0^3)/(3)+c\rbrack \\ =\lbrack30-(10.8)/(3)+c\rbrack-\lbrack0-0+c\rbrack \\ =30-3.6+c-c \\ =26.4\text{ m} \end{gathered}`