"Newton's law tells us that Force= Mass x Acceleration. We also know that Energy = Force x Distance and Pressure= Force/Area. Using these relationships and table I-1 [I'll type it out], derive (do math stuff) the dimensions of newtons, joules, and pascals in terms of the fundemental SI quantities."

Quantity - Unit - Symbol
length - meter - m
mass - kilogram - kg
time - second - s
elec. current - ampere - A
temperature - kelvin - K
lumin. int. - candela - cd
amount - mole - mol
plane angle - radian - rad
solid angle - steradian - sr

I have no clue how to go about deriving the dimensions of newtons, joules, and pascals. Could someone show me how, or at least point me in the right direction?

This is a physics question and not a chemistry question but I will try to get you started.
Force = mass x acceleration from above.
Force is in Newtons.
mass is in kilograms.
acceleration is in meters per second per second.
So kg*m/s^2 is a Newton.You can get some hints by going to and typing in 1 newton to kg. Also try joules to kg. I hope this gets you started.

Why is riding bike on the mud is harder then riding bike on the hard floor?

When you have a question it would be better to post it separately instead of piggy backing onto another post. The answer to your question is that the bike tire can't get good traction in the mud but it can on a hard floor. Read about the coefficient of friction.

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