If one horsepower is equal to 746 watts, how much horsepower does a highly trained athlete generate by doing 340 joules of work per second for an hourone

746 joules per second = 746 watts = 1 horsepower

340 joules per second = 340 watts = (340/746) = 0.456 horsepower

Power is a RATE or a SPEED of doing work.  

How long you do it doesn't matter.  

Just like 30 miles per hour doesn't change whether you do it for an hour or for 10 minutes.

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

after 28s,

m/s

which i would round to 150 m/s as my final answer