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Kinematic equations for uniformly accelerated motion

Motion in a straight line · Physics

Projectile launcher

Interactive 3D

Fire the cannon and watch the ball follow its true trajectory — range, apex and flight time update live.

Controls

Drag the sliders or type a value — the simulation updates live.

m/s
5m/s50m/s
°
10°80°

Study notes

A car starts from rest and accelerates uniformly at 2 m/s² for 6 seconds. Find (a) its final velocity and (b) the distance it covers. Step 1: List known values: u = 0 (starts from rest), a = 2 m/s², t = 6 s. Step 2: (a) Use v = u + at = 0 + 2 × 6 = 12 m/s. Step 3: (b) Use s = ut + ½at² = 0 × 6 + ½ × 2 × 36 = 36 m. Step 4 (check): Use the third equation v² = u² + 2as → 144 = 0 + 2 × 2 × s → s = 144/4 = 36 m. Both routes agree. Answer: final velocity 12 m/s, distance 36 m. This cross-check habit catches sign errors in harder problems.

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