You found that the displacement function is 𝑑(𝑡)=𝑒−𝑡+12sin(2𝑡)+2𝑡+𝑐𝑑(𝑡)=𝑒−𝑡+12sin(2𝑡)+2𝑡+𝑐.Remember that you were 22 km from your initial starting point when 𝑡𝑡 was 00.What is the value of 𝑐𝑐?
Question
You found that the displacement function is 𝑑(𝑡)=𝑒−𝑡+12sin(2𝑡)+2𝑡+𝑐𝑑(𝑡)=𝑒−𝑡+12sin(2𝑡)+2𝑡+𝑐.Remember that you were 22 km from your initial starting point when 𝑡𝑡 was 00.What is the value of 𝑐𝑐?
Solution
The displacement function is given as d(t) = e^(-t) + 1/2sin(2t) + 2t + c.
We know that at t=0, the displacement was 22 km. We can substitute these values into the equation to find the value of c.
So,
22 = e^(-0) + 1/2sin(20) + 20 + c 22 = 1 + 0 + 0 + c 22 = 1 + c
Subtract 1 from both sides to solve for c:
c = 22 - 1 c = 21
So, the value of c is 21.
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