# Motion in 1-Dimension

## Physics 231 with Doleans at Michigan State University *

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- Michigan State University
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- Physics 231
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- Motion in 1-Dimension

Motion in 1-Dimension • Dynamics: study of motion and of physical concepts such as force and mass • Kinematics: part of dynamics that describes motion • 1-D motion: motion along a straight line. Described in a frame of reference • Basic quantities to describe the motion: • position [m] • velocity [m/s] • acceleration [m/s2] • velocity and acceleration can be instantaneous or averaged over a certain amount of time • distance does not equal displacement • speed does not equal velocity • Scalar: has a mafnitude but no direction (ex. distance, speed...) • Vector: has a magnitude and a direction (ex. velocity) • Displacement is the change in position • Î”x = x(final) - x(initial) • SI unit (m) • displacement is the change in position between 2 instants, regardless of what happened in the middle • Distance does not equal displacement • distance is the accumulated travel over a certain time interval SI unit (m) • Average speed (scalar) • distance traveled divided by time interval • average speed = distance/Î”t • Average Velocity (vector) • displacement divided by time interval • v= Î”x/Î”t • Average acceleration (vector) • change in velocity during Î”t SI unit m/s2 • a = Î”v/Î”t • Equations at Constant Acceleration • a(final) = a (inital) SI unit m/s2 • v (final) = v(inital) + a(inital)*Î”t SI unit m/s • x(final) = x(inital) + v(inital)*Î”t + 0.5*a(inital)Î”t2 SI unit m • Other useful equations • x(final) = x(inital) + 0.5(v(final)+v(inital))*Î”t SI unit m • v(final)2= v(initial)2 + 2a(inital)Î”x SI unit m2/s2 • Freely Falling Objects • Objects moving freely under influence of gravity alone (no air resistance) • acceleration is constant and equal for all objects • at earth surface free fall acceleration is g=9.80 m/s2 • still called free fall when object is thrown upward initially • free fall is a particular case of constant acceleration with a=-g nothing more

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