The first kinematic equation is v equals u plus a t. This equation shows how velocity changes with time under constant acceleration. Here, v is final velocity, u is initial velocity, a is acceleration, and t is time. The graph shows velocity increasing linearly with time, where the slope represents acceleration.
Let's identify each variable in the equation. The letter u represents initial velocity, the starting speed of an object. The letter v represents final velocity, the speed after time t. The letter a represents acceleration, the rate of change of velocity. And t represents time, the duration over which the motion occurs. Watch how velocity increases as the car accelerates.
Now let's derive the first kinematic equation step by step. We start with the definition of acceleration as change in velocity over change in time. We substitute delta v as v minus u, and delta t as simply t. Next, we multiply both sides by t to get a t equals v minus u. Finally, we add u to both sides to isolate v, giving us our final equation: v equals u plus a t.
Let's solve an example problem. A car starts from rest and accelerates at 2 meters per second squared for 5 seconds. We need to find the final velocity. Given that initial velocity u equals zero, acceleration a equals 2 meters per second squared, and time t equals 5 seconds. Using our formula v equals u plus a t, we substitute the values to get v equals zero plus 2 times 5, which equals 10 meters per second.
The first kinematic equation v equals u plus a t has many practical applications. It's used in vehicle motion analysis, projectile motion calculations, free fall problems, sports physics, and engineering design. This equation represents a fundamental linear relationship between velocity, acceleration, and time under constant acceleration. It's one of four key kinematic equations that form the foundation of motion analysis in physics.