Straight Line Motion

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Straight Line Motion is the first lecture in the Mechanics section of PH1011. It covers a general insight as to how position relates to motion.

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Position, displacement and velocity
Position of a particle in straight line motion is given as a coordinate with respect to a 0 point. Coordinate systems must be specified and their x axis aligned suitably (usually along the direction of motion); the position of a particle as a function of time is x(t).

Displacement is the change in position. It is a vector quantity and simply given as the final position - initial position.

Average velocity is displacement/time.

Instantaneous velocity is the derivative of x(t) by t; v(t) = dx(t)/dt.

Speed is scaler; the total distance/time. The instantaneous speed is the magnitute of velocity and the average speed is 1/Δt∫titf|v(t)|dt.

Acceleration
Average acceleration is the change in velocity/change in time.

Instantaneous acceleration is the derivative of velocity; a(t) = dv(t)/dt.

The three equations of motion are still valid -
 * v(t) = v0 + at
 * x(t) = x0 + v0 + 1/2at2
 * v2t = v00 + 2a(x-x0)

Motion graphs
Position or displacement time graphs can be used to determine various factors in a system; the gradient of a point on the line gives the velocity of the body, and the curvature gives the acceleration. On a velocity time graph the slope is the acceleration, and the area under the line is the displacement.

Summary
Displacement -> velocity -> acceleration, by derivatives. Motion graphs can be used to determine values as well as equations.