Describing Motion: Position, Velocity, and Acceleration in One Dimension

Hi, I'm Lumi! Let's describe how things move along a straight line, like a cart on a track. Position tells you WHERE something is, measured from a chosen starting point, in meters. Velocity tells you how fast position is changing AND in which direction, in meters per second — so velocity is the rate of change of position. Acceleration tells you how fast the velocity itself is changing, in meters per second squared — so acceleration is the rate of change of velocity. Here's the chain: position changes give velocity, velocity changes give acceleration. Graphs make this visible. On a position-time graph, the curve bends when the cart accelerates — you can see it speeding up. On a velocity-time graph for constant acceleration, the data forms a straight line, and the slope of that line (rise over run = change in velocity over change in time) equals the acceleration. When acceleration stays constant, we can use kinematic equations. One key equation is v = v0 + a*t, where v0 is the starting velocity, a is acceleration, and t is time. Watch out for a sneaky idea: a positive velocity with a negative acceleration still means the object moves forward, just slowing down. Velocity and acceleration can point in opposite directions! If you ever feel stuck on a graph question, name the three quantities first, then ask which one the graph's slope is showing you. For equation problems, write down what you know (v0, a, t) before plugging in — that one step prevents most arithmetic errors.