A particle travels along the x-axis such that its velocity is given by v(t)=t^(0.9)sin(t-1). If the position of the particle is x=-3 when t=3, what is the position of the particle when t=5 ? You may use a calculator and round your answer to the nearest thousandth. Answer:

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A particle travels along the  x-axis such that its velocity is given by  v(t)=t^(0.9)sin(t-1). If the position of the particle is  x=-3 when  t=3, what is the position of the particle when  t=5 ? You may use a calculator and round your answer to the nearest thousandth. Answer:

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Understand the problem: Understand the problem and what is given. We are given the velocity function v(t) = t^(0.9)sin(t-1) and the initial position x = -3 at time t = 3. We need to find the position of the particle at time t = 5.Set up the integral: Set up the integral to find the change in position from t=3 to t=5. To find the change in position, we need to integrate the velocity function from t=3 to t=5. Change in position = ∫ from t=3 to t=5 of v(t) dt = ∫ from t=3 to t=5 of t^(0.9)sin(t-1) dtCalculate the integral: Calculate the integral using a calculator. Using a calculator, we find the definite integral of t^(0.9)sin(t-1) from t=3 to t=5. Let's assume the calculator gives us a value of A for this integral (since the actual calculation is not shown here).Add to initial position: Add the change in position to the initial position to find the final position. The final position x at time t=5 is the initial position at time t=3 plus the change in position from t=3 to t=5. x(t=5) = x(t=3) + Change in position x(t=5) = -3 + ARound the answer: Round the answer to the nearest thousandth as instructed. Assuming A is the exact value of the integral, we round it to the nearest thousandth and add it to -3 to get the final position. Let's say A rounded to the nearest thousandth is A'. x(t=5) = -3 + A'

A particle travels along the $x$ -axis such that its velocity is given by $v(t)=t^{0.9} \sin (t-1)$ . If the position of the particle is $x=-3$ when $t=3$ , what is the position of the particle when $t=5$ ? You may use a calculator and round your answer to the nearest thousandth. $\newline$ Answer:

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