#### To determine

**To estimate:**

The distance covered by the runner during 5 seconds.

#### Answer

45.23 m

#### Explanation

**1) Concept:**

i) The midpoint rule: ∫abfxdx≈∑i=1nf(xi-)∆x=∆x[fx1-+·····+fxn-]

Where ∆x=b-an and xi-=12xi-1+xi= midpoint of [xi-1,xi]

**2) Calculation:**

Apply the midpoint rule for the given values

∫abfxdx≈∑i=1nf(xi-)∆x=∆x[fx1-+·····+fxn-] Where ∆x=b-an and xi-=12xi-1+xi= midpoint of [xi-1,xi]

Here a=0, b=5, and let n=5

Therefore

∆x=b-an=5-05=510=1 Thus the intervals are [0,1],[1,2],[2,3],[3,4],[4,5] So

∑i=1nf(xi-)∆x≈∆xfx1-+·····+fxn-

=1 [ v0.5+v1.5+v2.5+v3.5+v4.5]

=1[4.67+8.86+10.22+10.67+10.76+10.81]

=45.23

**Conclusion:**

Therefore, thedistance covered by the runner during 5 seconds is ≈45.23 m