Question

Write a hypothesis about the effect of the angle of the track on the acceleration of the cart. Use the "if . . . then . . . because . . .” format and be sure to answer the lesson question: "How does an object's position and velocity change as the object accelerates?”

Answer 1

If the angle of the track increases, then the cart's acceleration down the track will increase, because the component of gravity acting along the incline (g·sinθ) becomes larger with steeper angles, producing a larger net force and thus a larger acceleration (neglecting friction).

How does an object's position and velocity change as the object accelerates?
- Velocity changes at the rate of the acceleration: v(t) = v0 + a t, so under constant acceleration the speed increases (or decreases) linearly with time.
- Position changes according to x(t) = x0 + v0 t + ½ a t^2, so displacement grows quadratically with time — the object covers increasingly larger distances in equal time intervals as it accelerates.
- Applied to the cart on a steeper track: larger a → velocity increases faster and the cart's position along the track increases more rapidly.