How do I solve this physics problems involving acceleration?

danmac7055: How do I solve this physics problems involving acceleration?
How can I solve this problem or atleast what are the steps I need to take?

Heres the problem:

Our hero, Noah Vale, is out for his afternoon constitutional when he spots the sultry Miss Terius standing at the bottom of a 1225m high cliff. At the top of the cliff is the arch villain, Rotcod Dam, who has dropped a boulder to strike the lovely young miss.
Noah, who is standing still 307.5m away from the cliff when the boulder starts downward, rushes to her resue. Noah, great athlete that he is, can accelerate at 10.00m/s/s, which he does until he reached his maximum velocity of 25.00 m/s. .He then races at the maximum velocity until he must stop to resue her. (Noah, being a truly great athlete can slow as fast as he can speed up, in other words his accceleration while slowing is -10.00m/s/s
Will Noah arrive in time to save our heroine, or will Miss Terius become another victim of physics?
The boulder accelerates at 9.800 m/s/s
You need to know that to solve the problem.

Answers and Views:

Answer by farwallronny
First, let’s find out how long it will take for the boulder to reach the bottom of the cliff:
1225=(9.8/2)*(t^2)=4.9*t^2
1225/4.9=t^2
sqrt(1225/4.9)=t=15.81 seconds
Our hero must reach her in under 15.81 seconds.

Now, let’s figure out how long it will take him to cover the 307.5 meters.
First, how much time and distance are needed to reach his top speed:
Clearly, he accelerates to his top speed in 2.5 seconds.
The distance covered during his acceleration is:
d=a/2*t^2=10/2*2.5^2=5*6.25=31.25 meters.

Decelerating will take an equal time and distance.

So, Noah runs the remaining 245 meters at a constant rate of 25 meters/second.
This will take 9.8 seconds: 245/25=9.8 seconds.

His total run takes 14.8 seconds: 9.8+(2.5*2)=14.8

Yes, Noah save our hapless damsel with a huge 1.01 seconds to spare.
(rah rah)