ap/ib physics B dimensionlly correct equations??

Question

i have some practice questions on dimensionally correct equations that i just can't understand.

1. v^2 = v0^2 + 2ax

and

2. x = v0t + 1/2 * a^2 * t^2

i know x =length (L)
and a = acceleration (L/T^2)
and v & v0 = velocity (L/T)
and t = time (T)

i just don't understand how to put everything together.work would be appreciated due to the fact that i'm trying to figure out how to do this problem, i don't want just the answer. THANKS! :)

Answer 1

x - meters
v - meters/seconds
a - meters/seconds^2
t - seconds

v^2 - meters^2 / seconds^2
a*x = meters^2 / seconds^2

v*t = meters/seconds * seconds = meters

Your second equation should read
1/2 * a*t^2

Answer 2

Replace the variables with their units:

v^2 = v0^2 + 2ax ---> m^2/s^2 = m^2/s^2 + m/s^2 * m = m^2/s^2


x = v0T +1/2 at^2 ---> m = m/s * s + m/s^2 * s^2 = m

I used meters and seconds instead of L and T but you get the idea.

Answer 3

You need to ensure that the dimensionality of each term that's added is the same, and also that it's the same across the equals sign.

So... in 1., show that the dimensions of v^2, Vo^2 and ax are the same. The first two are trivial.. so you only need to show that acceleration (L/T^2) x distance (L) has the same dimensionality as V^2.