Grade 12 Math · Velocity as the derivative
Acceleration is the rate of a rate
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Acceleration is the rate of a rate

Velocity is the rate of change of position. Take the rate of change of THAT and you have acceleration: a=ΔvΔta = \dfrac{\Delta v}{\Delta t}, and in the notation waiting for you in MCV4U, a=dvdta = \dfrac{dv}{dt}. It is the slope of the velocity–time graph — the very quotient you computed in the last lesson, with velocity sitting on the y-axis. Its unit, m/s2\mathrm{m/s^2}, is best read as metres per second, per second: how much speed is gained every second.

Rearranged forward, that gives v=v0+atv = v_0 + at — read v equals v-nought plus a t. Naming the letters: vv is the final velocity in m/s, v0v_0 the initial velocity in m/s, aa the acceleration in m/s2\mathrm{m/s^2}, and tt the elapsed time in seconds; solve for whichever one the question withholds.

Now look at its shape, because this is the nugget: v=v0+atv = v_0 + at is y=b+mxy = b + mx in disguise. The starting velocity is the intercept, the acceleration is the slope, and time is the horizontal axis. Uniform acceleration means a straight velocity line, and everything you know about straight lines transfers intact. Push the units through any rearrangement you try: if they refuse to cancel into the answer's unit the rearrangement is wrong, no appeal — though units that do work out never prove you right. The check runs one way only.