Help with Problem: Find Distance Travelled in First 5.0s

[Alanf718]

I was doing this problem, and now I wonder where I went wrong

The problem states
A ball starts from rest and rolls down a hill iwth uniform acceleration, traveling 150m during the second 5.0s of its motion. How far did it roll during the first 5.0s of motion.

This is what I did

x = 150m
t = 5.0s
with that data I got the velocity for stage 2
v = 30m/s

with that I tried to determine the acceleration so
V = Vo + at
30m/s = 0m/s + a(10s);
I got a = 3m/s

then I tried getting the x with
X = Xo + Vot + 1/2(a*t^2);
X = 0 + 0 + 1/2(3m/s*(5^2));
and I got X to be 37.5m but the book says the answer is 50m where did I go wrong?

 

[radou]

...This is what I did

x = 150m
t = 5.0s
with that data I got the velocity for stage 2
v = 30m/s

This would be correct if there was no acceleration, i.e. if the velocity had been constant. Write down the equation of displacement for the second interval of 5 seconds first. Then see which parts of the equation you can (and need) to express with information you know about the first 5 seconds. You'll end up having only one unknown, which will be the acceleration. Then you can easily calculate the displacement in the first 5 seconds.

 

[Alanf718]

Iam ending up with 2 unknowns
writing it as
X- Xo = Vot + 1/2(a*t^2);

That leaves me with Vo unknown as well as the a, I can't solve it with 2 unkowns :-( and I don't know How I would get the initial velocity at stage two to solve this.[EDIT]
Forget it i got the answer I replace Vo with a*t in other words a*5 thanks for the help!

 

[radou]

Iam ending up with 2 unknowns
writing it as
X- Xo = Vot + 1/2(a*t^2);

That leaves me with Vo unknown as well as the a, I can't solve it with 2 unkowns :-( and I don't know How I would get the initial velocity at stage two to solve this.

Okay, the equation of displacement for the 'second' 5 sec is x = x0 + v0*t + 1/2*a*t^2, hence 150 = x0 + v0*5 + 1/2*a*5^2. What does xo equal? And what about v0?