Launch Control
Braking, vertical motion and interception.
Motion scene
Choose a positive direction. The signs of displacement, velocity and acceleration follow that choice.
Displacement–time
Velocity–time
The physics
Uniform acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t.
Braking: thinking distance = u × reaction time; braking distance = u²/(2b), where b is the positive deceleration magnitude. The vehicle moves at constant speed during reaction time and then decelerates uniformly.
Vertical launch: with upwards positive, a = −9.81 m/s². With downwards positive, a = +9.81 m/s². Air resistance is neglected. The ground and launch point are at the same height.
Interception: two objects meet when their displacements measured from the same origin are equal at the same time. The second object starts from rest after a delay and then accelerates uniformly.
Distance is always non-negative. Signed displacement and velocity depend on the chosen axis.
All six motion challenges completed.