Uniformly Accelerated Motion


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Uniformly Accelerated Motion

 

the motion of a point such that its tangential acceleration wτ 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 + wτt s = v0t + wτt2/2

where ν0 is the initial speed of the point. When ν and wT 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

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