Question

In part A, I found:

integral v(t)|t=0 to t=4 = 20

integral v(t)|t=4 to t=7= -4

integral v(t)|t=7 to t=10 = -20

integral v(t)|t=0 to t=10 = -4

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Part B asks:

If s'(t)=v(t), then s(t) is the position of the runner at time t. Let s(0)=−6, determine the following values.

s(4)= ?

s(5)=?

s(7)=?

s(9)=?

Answer 1

Im not sure if theres an equation for the v(t) you`re given but this is my take:

if integral v(t) from 0-4 =>20, then from position -6, the person travelled 20 units :

s(4) = 14

for s(5), from t = 4 to t = 7, theres a linear slope of -4/3, so(-4/3)(1 second) = -4/3

s(5) = 14- 4/3 = 12.67

for s(7) after t = 4 to t=7, the slope is -4/3, in other words it went down 4 units over a span of 3.

∴ s(7) = 14 -4 = 10

for s(9), from t=7 to t = 10 the slope is -20/3,(-20/3)(2 seconds)

s(9) = 10 - 2(20/3) = -10/3 = -3.33

Hope that helps.