Velocity–Time Relation

Gives the velocity of an object after it has been accelerating at a constant rate for a time t. Use it whenever you know initial velocity, constant acceleration, and elapsed time and need the final velocity.

Applies to any object moving with constant (uniform) acceleration in a straight line. Works for deceleration too — just treat a as negative.

Invalid when acceleration varies with time or position. Does not apply to rotational motion without adapting to angular quantities.

Forgetting that v_0 is the velocity at the start of the interval, not necessarily zero. Using the wrong sign for a — deceleration must be entered as negative if v_0 is positive. Confusing elapsed time t with a clock reading when the motion started at some t > 0.

• motion in a straight line

• [easy] A car moves along a straight highway at a constant velocity of 25 m/s. How far does it travel in 8 s…
• [medium] A train leaves a station at 5 m/s and accelerates uniformly at 2 m/s² for 12 seconds. Find the train…
• [hard] A driver is travelling at 30 m/s when they spot a hazard. Their reaction time is 0.8 s, after which …
• [challenge] Train A starts at position x = 0 and travels in the +x direction at 20 m/s. At the same moment, Trai…
• [exam] Car B has a 50 m head start and moves at a constant 15 m/s. Car A starts from rest at the same momen…