Finding distance from acceleration as a function of s Watch

stley
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Hello,

I'm having alot of trouble with this question:

A shuttle train has an acceleration given by a = (0.10 +0.004s) m/s2 where s is distance measured in m. Calculate the distance s at which its speed v is 51 km/h. Give your answer in m.

I'm new to these types of questions and don't really know what to do! I've tried intergrating a but it isn't really working. Any help is appreicated espically if you show all the steps

Thanks alot
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DarkEnergy
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(Original post by stley)
Hello,

I'm having alot of trouble with this question:

A shuttle train has an acceleration given by a = (0.10 +0.004s) m/s2 where s is distance measured in m. Calculate the distance s at which its speed v is 51 km/h. Give your answer in m.

I'm new to these types of questions and don't really know what to do! I've tried intergrating a but it isn't really working. Any help is appreicated espically if you show all the steps

Thanks alot
This might be wrong, so someone please correct me if it is.

You know:
a = (0.1 + 0.004s) and
v = 51km/h --> 51000/(60*60) = ~14ms-1
and you need s

Assuming the shuttle train is starting from rest, u = 0

So we can use a suvat equation:
v2 = u2 + 2as

As u = 0, we are left with:
v2 = 2as

Plug in the known values. You end up with a quadratic, which can then be solved for s.
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