anonymous
  • anonymous
A particle moves along a line. The particles position,s, in centimetres at t seconds is modelled by s(t)=t^3-9t^2+24t+20,where t is greater than or equal to zero. What is the total distance travelled by the particle in the first 8 seconds??
Calculus1
schrodinger
  • schrodinger
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anonymous
  • anonymous
We know that the expression \[s(0) +\int_{0}^{8} |v(t)| dt\] will give the total distance traveled. We can see from the position function that \[s(0)=20\]. From the graph of the velocity function, we can evaluate the definite integral by breaking it into parts "above" and "below" the x-axis. The graph of velocity crosses the x-axis at x=2 and x=4. Thus, we can find the total distance traveled by evaluating the following expression: \[20+\int_{0}^{2} v(t) dt - \int_{2}^{4} v(t) dt + \int_{4}^{8} v(t) dt\]

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