What Do Position and Velocity Graphs Tell You About Motion?
How Do Position, Velocity and Acceleration Graphs Connect?
In short: With constant acceleration, x(t) = x₀ + v₀t + ½at² is a parabola, while v(t) = v₀ + at is a straight line whose slope is the acceleration. The slope of the x(t) graph at any moment is the velocity. When v and a have opposite signs, the object slows down, stops for an instant at v = 0, then reverses.
Common doubts
If v = 0, is a = 0 too? No. With the default settings the object stops at t = 5 s, but its acceleration is still −1 m/s². Velocity is zero only for an instant before the object turns around.
Why is the x(t) graph curved while v(t) is straight? Velocity changes at a steady rate, so the position changes by a different amount every second. That makes the x(t) graph a parabola.
Can an object speed up with a negative acceleration? Yes, if its velocity is also negative. The object speeds up when v and a have the same sign and slows down when the signs differ.
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