Kinematic relation between height and speed under constant acceleration

Steps:

• Ball dropped from rest: initial speed v=0, initial height h=h₀, acceleration a=g downward.
• Speed v=gt, so time t=v/g.
• Height h=h₀ - (1/2)gt² = h₀ - (1/2)g(v/g)² = h₀ - v²/(2g).
• Thus, h decreases quadratically with v: straight line if plotted vs v², curved downward vs v.

Why C is correct:

• C shows h decreasing nonlinearly (parabolically) with increasing v, matching h = h₀ - v²/(2g) from kinematics.

Why the others are wrong:

• A: Linear decrease implies constant speed, violating acceleration.
• B: Constant h ignores motion entirely.
• D: Increasing h contradicts downward fall.

Final answer: C