How to find the speed when acceleration and time is given

Finding speed from acceleration and time alone is impossible without knowing the initial velocity—this is a key conceptual point students often miss. The formula v = u + at requires three inputs to produce one output, so having only a and t leaves initial velocity (u) as an unknown variable. If a problem states only "acceleration is 5 m/s² for 10 seconds," you can calculate that speed changed by 50 m/s, but cannot determine the actual final speed without knowing the starting speed.

However, if the context implies starting from rest (common in many physics problems), then u = 0 simplifies the formula to v = at. A dropped object falling for 3 seconds under gravity (a = 9.8 m/s²) reaches v = 9.8(3) = 29.4 m/s. A car accelerating from a traffic light at 2 m/s² for 7 seconds achieves v = 2(7) = 14 m/s. Whenever a problem mentions "starting from rest," "dropped," "released," or "launched from standstill," the u = 0 assumption is valid.

For problems where initial velocity isn't explicitly stated or obviously zero, you must request additional information or recognize that multiple solutions exist. A physics problem asking "what speed does an object reach after accelerating at 3 m/s² for 5 seconds" is technically unsolvable without clarification—the answer could be 15 m/s (if u = 0), 25 m/s (if u = 10 m/s), or any value depending on initial conditions. This highlights why problem-solving in physics requires complete information: missing even one variable makes calculations impossible or ambiguous.