Question

A car runs at a velocity of v(t) = e-t + 3t + 1, where t is measured in seconds. Find the distance travelled by the car in the first second?

Answer 1

Curiousmathstudent lets be curious about it .... and solve together !

Answer 2

The distance traveled during a small dt time is given by:
\[distance = \int_{t1}^{t2}v(t)dt\]
Substituting, we get

\[distance = \int_{0}^{1}(e^{-t}+3t+1)dt = [-e^{-1}+\frac{3\times1^2}{2}+1 - -e^{-0}+\frac{3\times0^2}{2}+0]\]

Simplify to get your answer :)

Hope this helps.

Answer 3

Gee thanks (:

Answer 4

You are most welcome :)