Answer:
(a) 2 feet.
(b) 2 feet.
Step-by-step explanation:
We have been given that the velocity function
in feet per second, is given for a particle moving along a straight line.
(a) We are asked to find the displacement over the interval
.
Since velocity is derivative of position function , so to find the displacement (position shift) from the velocity function, we need to integrate the velocity function.




Using power rule, we will get:
![\left[\frac{t^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}}\right] ^4_1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cfrac%7Bt%5E%7B-%5Cfrac%7B1%7D%7B2%7D%2B1%7D%7D%7B-%5Cfrac%7B1%7D%7B2%7D%2B1%7D%7D%5Cright%5D%20%5E4_1)
![\left[\frac{t^{\frac{1}{2}}}{\frac{1}{2}}}\right] ^4_1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cfrac%7Bt%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%5Cright%5D%20%5E4_1)

Therefore, the total displacement on the interval
would be 2 feet.
(b). For distance we need to integrate the absolute value of the velocity function.


Since square root is not defined for negative numbers, so our integral would be
.
We already figured out that the value of
is 2 feet, therefore, the total distance over the interval
would be 2 feet.
Answer:slope=10.000/2.000=5.000
x-intercept=2/5=minus 0.40000
y-intercept=2/1=2.00000
Step-by-step explanation:
Assuming that the triangles are congruent, you can just look at the parts on each triangle to find the parts on the other triangle. The answers are yes, yes, and no. The triangles are obviously not drawn to scale, so just remember to never rely on it being so.