Question

Calculate total distance?

Answer 1

Simply find the area under the velocity curve. Over the first 3 second interval, the area is that of a trapezoid with bases 2 and 5, so that area/distance traveled is
`\left(\frac{2+5}2(\rm m)/(\rm s)\right)\cdot(3\,\mathrm s)=\frac{21}2\,\mathrm m`. For the last 4 seconds, the area/distance is
`\left(5(\rm m)/(\rm s)\right)(4\,\mathrm s)=20\,\mathrm m`.

Then the total distance traveled is

`\frac{21}2\,\mathrm m+20\,\mathrm m=\frac{61}2\,\mathrm m=30.5\,\mathrm m`