The physics
Slopes: the slope of x-t is the velocity. The slope of v-t is the acceleration.
Areas: the area under v-t is the displacement. The area under a-t is the change in velocity. Area below the time axis counts as negative.
v = dx/dt a = dv/dt Δx = ∫v dt Δv = ∫a dt
Distance adds every area as positive. Displacement keeps the signs.