The velocity of a car is given by v(t)= 20(x+sin(x)0 miles per hour.
a. how far does the car travel between t=1 and t=3.2 hours?
To find the distance traveled by the car between t = 1 and t = 3.2 hours, we first need to find the expression for the displacement function. The displacement function can be obtained by integrating the velocity function with respect to time.
Given the velocity function v(t) = 20(x + sin(x)), we integrate it with respect to t to get the displacement function:
s(t) = ∫v(t) dt
= ∫20(x + sin(x)) dt
To integrate this function, we need to know the limits of integration. In this case, we are interested in finding the distance traveled between t = 1 and t = 3.2 hours. So we integrate the velocity function with these limits:
s(t) = ∫[1 to 3.2] 20(x + sin(x)) dt
Now, we can solve this integral to find the displacement function. However, it seems like there might be an error in the provided velocity function. The presence of 'x' as part of the velocity equation might be unintended or represent a different variable. Could you please clarify the equation or provide additional information?