Thus, acceleration can be expressed as the second derivative of the displacement.
Newton’s second law (F = ma) can be expressed in differential calculus as follows:
m
dv
—
dt
= For m
d
2
x
—
dt
2
= F
Using the Area of a V-T Graph to Find the Distance
Traveled by an Object
Next, let’s examine how we can find the distance an object travels if we already know its
velocity (see page 54). When the velocity is uniform, we know that the following equation
holds true, and we can find the distance traveled (∆x) over a change in time (∆t).
For a velocity that’s changing magnitude, we can find an approximation by summing up ...
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