At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer
Average velocity in the first 2 seconds = 16 ft/s
Explanation
The average value of a function over an interval [a, b] is given as
[tex]\text{Average value of the function = }\frac{1}{b-a}\int ^b_af(x)dx[/tex]The integral is evaluated over the same interval [a, b]
Since we are asked to find the average velocity over the first 2 seconds, we need to first obtain the funcion for th object's velocity.
Velocity = (dh/dt)
h(t)= -16t² + 48t + 120
Velocity = (dh/dt) = -32t + 48
So, we can then find the average velocity over the first 2 seconds, that is, [0, 2]
[tex]\begin{gathered} \text{Average value of the function = }\frac{1}{b-a}\int ^b_af(t)dt \\ a=0,b=2,f(t)=-32t+48 \\ \text{Average Velocity = }\frac{1}{2-0}\int ^2_0(-32t+48)dt \\ =\frac{1}{2}\lbrack-16t^2+48t\rbrack^{2_{}}_0 \\ =\frac{1}{2}\lbrack-16(2^2)+48(2)\rbrack_{} \\ =0.5\lbrack-16(4)+96\rbrack \\ =0.5\lbrack-64+96\rbrack \\ =0.5\lbrack32\rbrack \\ =16\text{ ft/s} \end{gathered}[/tex]Hope this Helps!!!
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
