Question
Given the velocity function $v$ of an object moving along a line, explain how definite integrals can be used to find the displacement of the object.
Step 1
Step 1: First, we need to understand that the velocity function $v(t)$ describes the rate of change of the object's position with respect to time. Show more…
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Given the velocity function v of an object moving along a line, explain how definite integrals can be used to find the displacement of the object. Choose the correct answer below. A. The displacement between t = a and t = b, [a,b], is ∫[b to a] |v(t)| dt. B. The displacement between t = a and t = b, [a,b], is ∫[a to b] |v(t)| dt. C. The displacement between t = a and t = b, [a,b], is ∫[a to b] v(t) dt. D. The displacement between t = a and t = b, [a,b], is ∫[b to a] v(t) dt.
Velocity to position Given the following velocity functions of an object moving along a line, find the position function with the given initial position. Then graph both the velocity and position functions. $$v(t)=2 \sqrt{t} ; s(0)=1$$
Applications of the Derivative
Antiderivatives
Given the following velocity functions of an object moving along a line, find the position function with the given initial position. $$v(t)=2 \sqrt{t} ; s(0)=1$$
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