A car on the freeway accelerates according to $a = 17 \cos(\pi t)$, where $t$ is measured in hours. Set up and solve the differential equation to determine the velocity (in mph) of the car if it has an initial speed of 57 mph.
$v(t) =$ mph
After 40 minutes of driving, what is the driver's velocity (in mph)? (Round your answer to two decimal places.)
mph
Find the expression for the distance (in miles) the car has traveled in time $t$, assuming an initial distance of 0.
$d(t) =$ mi
How long does it take the car to travel 100 miles? Round your answer to hours and minutes.
hr min
Find the total distance (in miles) traveled in the first hour. (Round your answer to three decimal places.)
m