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x = x0 + v0 * t + 1/2 * constant acceleration * t^2

So this is supposed to be very very simple physics, but I still feel like there's a part of this equation I don't fully understand. The first term is the initial position of the body at t=0. The second term is the initial velocity at t=0, multiplied by the time elapsed since then. So far so good. Now, it's the third term I have trouble interpreting. I know it comes from integrating the acceleration function, but

I tried to reason it the following way: Let's assume a=2 m/s^2, and for the sake of simplicity make both the initial position and velocity zero. Ok, so if I want to know the position of this body at t=1, then given that constant acceleration, velocity at t=1 will be 2 m/s. So the body should have had a displacement of 2 metres, right?

But if I plug in the values in the formula, I'd get x = 1/2 * 2 m/s^2 * 1 s^2 = 1 metre. Why is this the case?

I know it must be pretty stupid, but I can't figure out what's wrong with my reasoning.

Thanks in advance!

So this is supposed to be very very simple physics, but I still feel like there's a part of this equation I don't fully understand. The first term is the initial position of the body at t=0. The second term is the initial velocity at t=0, multiplied by the time elapsed since then. So far so good. Now, it's the third term I have trouble interpreting. I know it comes from integrating the acceleration function, but

*why*exactly is it so?I tried to reason it the following way: Let's assume a=2 m/s^2, and for the sake of simplicity make both the initial position and velocity zero. Ok, so if I want to know the position of this body at t=1, then given that constant acceleration, velocity at t=1 will be 2 m/s. So the body should have had a displacement of 2 metres, right?

But if I plug in the values in the formula, I'd get x = 1/2 * 2 m/s^2 * 1 s^2 = 1 metre. Why is this the case?

I know it must be pretty stupid, but I can't figure out what's wrong with my reasoning.

Thanks in advance!