ACCELERATION

time rate at which a velocity is changing. Because velocity has both magnitude and direction, it is called a vector quantity; acceleration is also a vector quantity and must account for changes in both the magnitude and direction of a velocity. The velocity of a point or an object moving on a straight path can change in magnitude only; on a curved path, it may or may not change in magnitude, but it will always change in direction. This condition means that the acceleration of a point moving on a curved path can never be zero. If the velocity of a point moving on a straight path is increasing (i.e., if the speed, which is the magnitude of the velocity, is increasing), the acceleration vector will have the same direction as the velocity vector. If the velocity is decreasing (that is, the point or object is decelerating), the acceleration vector will point in the opposite direction. The average acceleration during a time interval is equal to the total change in the velocity during the interval divided by the time interval. The acceleration at any instant is equal to the limit of the ratio of the velocity change to the length of the time interval, as the time interval approaches zero. When a point moves on a curved path, the component of the acceleration that results from the change in the direction of the velocity vector is perpendicular to the velocity vector and is directed inward, to the concave side of the path; its magnitude is given by the square of the velocity divided by the radius of curvature r of the path: v2/r. The change in the magnitude of v may be represented by another vector (that is, a second component of the acceleration) collinear with v and in the same direction if v is increasing and the opposite direction if v is decreasing. If velocity is stated in metres per second, acceleration will be stated in metres per second per second.