The constant-acceleration kinematic equations can only be used with particles or objects modeled as particles.

Since we're dealing with a particle, it is permissible to use the constant-acceleration kinematic equations.

We'll use the kinematic equations to check if acceleration is constant across intervals.

So we use:

a_x = Δv_x/Δt

From t = 0 to t = 15 s, we have a₁ = (45 m/s - 0 m/s)/(15 s - 0 s) = 3 m/s²

From t = 15 s to t = 30 s, we have a₂ = (90 m/s - 45 m/s)/(30 s - 15 s) = 3 m/s²

From 0 to 30s, we have a₃ = (90 m/s - 0 m/s)/(30 s - 0 s) = 3 m/s²

The three intervals have equal acceleration.

Thus, a₁ = a₂ = a₃ = 3 m/s².

The particle has a uniform acceleration inside the accelerator.

This is because the change in speed after every second is constant and is 3 m/s².

If a₁, a₂, and a₃ are not equal, we conclude that acceleration varies with time.