Acceleration

Objective: Compute change in velocity divided by time.

Average acceleration in one dimension is a_avg = (v_f − v_i)/Δt, with SI unit m/s². A velocity change from 2 m/s to 10 m/s over 4 s corresponds to +2 m/s². Acceleration describes a change in velocity, which can reflect a change in speed, direction, or both. A negative acceleration is acceleration in the negative coordinate direction and is not automatically slowing down: an object moving left and accelerating left can gain speed. Acceleration calculations require velocities in the same reference frame and a positive, stated time interval.

Objective: Determine speeding up or slowing down from velocity and acceleration directions.

In one-dimensional motion, speed increases when acceleration and velocity have the same sign and decreases when their signs oppose, over an interval where the velocity does not cross zero. For v = −6 m/s and a = +2 m/s², the object initially slows while moving in the negative direction. If the acceleration continues long enough, velocity can reach zero and reverse; after reversal it speeds up in the positive direction. A constant acceleration model gives v_f = v_i + aΔt, but its use requires approximately constant acceleration over the interval. Turning in two dimensions also changes velocity even when speed is steady.

Objective: Describe gravitational acceleration and its assumptions.

Near Earth’s surface, freely falling objects have approximately constant downward acceleration of magnitude 9.8 m/s² if air resistance is negligible. This is an idealized model, and actual motion depends on drag and conditions. If upward is positive, acceleration is about −9.8 m/s² both while an object travels upward and while it travels downward; at the highest point, instantaneous vertical velocity is zero but acceleration is not. Objects of different masses have the same ideal free-fall acceleration in the same gravitational field when drag is neglected. Motion calculations should state the coordinate direction and approximation used.