Integration Problem?

Question

A car accelerates from 0mph to 35 mph. Its velocity at time t is v(t)=5t mph where t is in seconds. Use an integral to find the total distance in miles it travels during its acceleration. (Hint: work with seconds not hours.) The answer is in seconds per hour

miles per second, my bad :)

Answer 1

You're integrating with respect to t, so the bounds of the integration are t = 0 seconds to t = 7 seconds (it takes 7 seconds to get to 35 mph).

And then, as you point out, you need to convert the velocity from miles per hour to miles per second.

5t miles/hour × (1 hour/60 minutes) × (1 minute/60 seconds) = t/720 miles/sec

7
∫ t/720 dt = [1/720 t²] from 0 to 7 = [1/720 (7² - 0²)] = 0.068 miles
0

That's about 360 feet, which is less than I expected, but I think it's right.