Acceleration is the change in velocity of an object by either changing the objects speed or direction of motion.
On a plot describing the velocity of an object versus time, the slope of the graph, Δv/Δt, is the average acceleration of the object.
Aavg = Δv/ Δt
This equation can also be written vf = vi + a(Δt)
The diagram below is the velocity/time graph of an object that acclerates uniformly from vi to vf. The shaded area represents the displacement of the object.
If we break this area up into two regions (see below) calculating the area of the region is simple. The blue region has an area of (vi)(Δt) while the blue area has an area of 1/2(vf-vi))(Δt).
The total area of the both the red and blue regions = (vi)(Δt) + 1/2(vf-vi))(Δt). This also represents the displacement of the object.
Δd = (vi)(Δt) + 1/2(vf-vi))(Δt).
Substituting in vi + a(Δt) for vf we get ...
Δd = (vi)(Δt) + 1/2(vi + a(Δt) - vi)(Δt).
Simplifiying, we get
Δd = (vi)(Δt) + 1/2a(Δt)^2.
Equations so far:
The last equation listed above is derived from combining other eqations and is not directly derived from the d/t graph or v/t graph. See the textbook for the derevation in section 2.5
Homework: Read 2.4-2.5
Do Problems - Page 39-40 - 21,23,25,27,and 31
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