Question

Consider an object moving along a line with the following velocity and initial position. v(t) = 9 -12 on [0, 4); $(0) = -1 Determine the position function for t20 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the two methods. To determine the position function for t20 using the antiderivative method, first determine how the velocity function and the position function are related. Choose the correct answer below. O A. The position function is the absolute value of the antiderivative of the velocity function. OB. The position function is the antiderivative of the velocity function. OC. The velocity function is the antiderivative of the absolute value of the position function. OD. The position function is the derivative of the velocity function. Which equation below will correctly give the position function according to the Fundamental Theorem of Calculus? O A. s(t) = S(0) + v(t)dt OB. 8(0) = s(t) + [v(x)dx OC Mt)=(0) Svensk D." - Sve Determine the position function for to using both methods. Select the correct choice below and fill in the answer boxes) to complete your choice. 다. OA. The same function is obtained using each method. The position function in (0) O B. Different functions are obtained using each method. The position function obtained using the antiderivative method is st)= and the position function obtained using the Fundamental Theorem of Calculus is -

Answer 1

The 3 rate of Change of position is called displacemen It is denoted by Oy Sct) g dependent variable t Inclependent Valiaha. The rate of change of Displacement is Velocity ds at vet) at Apply Integration or antidifferentiation on Both sides 5 ds = Sucthat Is 8 = Suctsalt Displacement = antidkrivative of Velocity of position Given Vct)= 9-t S= Suct at Ja-tit 2+1 .t 2+1 Sct) t- +3 Define over (0,4] 519-a) at [fundenental Theron of calces 4 3- at ta $(+) 108-69 ay 3 $(0) = 960)-(0'+c