110. Comparing distances Suppose two cars started at the same time and place (t = 0 and s = 0). The velocity of car A (in mi/hr) is given by
u(t) = 40 / (t + 1) and the velocity of car B (in mi/hr) is given by v(t) = 40 * e^(-t/2).
b. After t = 3 hr, which car has traveled farther?

Fuel consumption A small plane in flight consumes fuel at a rate (in gal/min) given by

R'(t) ={ 4t^{1/3} if 0 ≤ t ≤ 8 (take-off)

2 if t> 0 (cruising)

a. Find a function R that gives the total fuel consumed, for 0≤t≤8.

2–3. Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s.

d. Determine the position function s(t) using the Fundamental Theorem of Calculus (Theorem 6.1). Check your answer by finding the position function using the antiderivative method.

v(t) = 12t²-30t+12, for 0 ≤ t ≤ 3; s(0)=1

Flow rates in the Spokane River The daily discharge of the Spokane River as it flows through Spokane, Washington, in April and June is modeled by the functions

r1(t) = 0.25t²+37.46t+722.47 (April) and

r2(t) = 0.90t²−69.06t+2053.12 (June), where the discharge is measured in millions of cubic feet per day, and t=0 corresponds to the beginning of the first day of the month (see figure).

a. Determine the total amount of water that flows through Spokane in April (30 days). 

Flow rates in the Spokane River The daily discharge of the Spokane River as it flows through Spokane, Washington, in April and June is modeled by the functions

r1(t) = 0.25t²+37.46t+722.47 (April) and

r2(t) = 0.90t²−69.06t+2053.12 (June), where the discharge is measured in millions of cubic feet per day, and t=0 corresponds to the beginning of the first day of the month (see figure).

c. The Spokane River flows out of Lake Coeur d’Alene, which contains approximately 0.67mi³ of water. Determine the percentage of Lake Coeur d’Alene’s volume that flows through Spokane in April and June.

The velocity ($\mathrm{mi}$/$hr$) of a drone flying in the air is given by $v\left(t\right)=12+4t^2$ for $0\le t\le 4$ hours. Let $s\left(0\right)=0$.

Determine $s\left(t\right)$ for $0\le t\le 4$.

The velocity ($\operatorname{mi}$/$hr$) of a drone flying in the air is given by $v\left(t\right)=12+4t^2$ for $0\le t\le4$ hours. Let $s\left(0\right)=0$.

How far does the drone travel during the first hour?

The velocity ($\operatorname{mi}$/$hr$) of a drone flying in the air is given by $v\left(t\right)=12+4t^2$ for $0\le t\le4$ hours. Let $s\left(0\right)=0$.

How far has the drone traveled by the time it has reached $48\mathrm{mi}$/$hr$?

Suppose that a particle travels along the $x$-axis and its velocity is given by $v\left(t\right)=2\cos t$ for $0\le t\le 2\pi$.

Find the particle's displacement on $[0,\frac{5\pi }{4}]$