How to find the dimensions of a particle moving in one dimension?

[kratos]

So a particle of mass M is moving in one dimension given by:
x(t) = (alpha)t^2 + (beta)t + (gamma)

where alpha, beta, gamma are non zero constants.

What are the dimensions of the alpha, beta, gamma?

Either the answer is staring right at my face or my physics is rusty :/

 

[knowlewj01]

This looks like one of the equations of motion for a particle moving in the x direction.

x(t) = ut + \frac{at^2}{2}

 

[Redbelly98]

So a particle of mass M is moving in one dimension given by:
x(t) = (alpha)t^2 + (beta)t + (gamma)

where alpha, beta, gamma are non zero constants.

What are the dimensions of the alpha, beta, gamma?

Either the answer is staring right at my face or my physics is rusty :/

Welcome to Physics Forums.

Okay, let's look at the beta term as an example:

The units of beta·t must agree with the units of x. So we can write

beta·t ~ x​

Where "~" means they have the same units, not that they are equal. But, we can solve this as if it were an equation. So, solving for beta, what do you get?