Uniformly Accelerated Motion

the motion of a point such that its tangential acceleration w_τ is constant; in the case of uniformly accelerated rectilinear motion, the point’s acceleration w is constant. The speed ν of the point t sec after uniform acceleration begins and the point’s distance s from its initial position—s being measured along the point’s path—are determined for uniformly accelerated motion by the equations

ν = ν₀ + w_τt s = v₀t + w_τt²/2

where ν₀ is the initial speed of the point. When ν and w_T are of the same sign, acceleration occurs; when they are of opposite sign, deceleration occurs.

When a rigid body undergoes uniformly accelerated transla-tional motion, the above definitions apply to each point of the body. A body may also undergo uniformly accelerated rotation about a fixed axis; in this case, the body’s angular acceleration;ε is constant, and the angular speed ω and angular displacement ɸ of the body are

ω = ω₀ + ∊ t ɸ = ω₀t t + ∊t²/2