Answer:
[tex]a'(t) = 2k*v'(t)*v(t)[/tex]
Step-by-step explanation:
According to the data provided, the acceleration can be modeled by the following equation:
[tex]a(t) = kv(t)^2[/tex]
Where a(t) is the acceleration as a function of time, and v(t) is the velocity ad a function of time.
Applying the chain rule, the differential equation, with proportionality constant k, is:
[tex]\frac{d(a(t))}{dt}=\frac{d(kv(t)*v(t))}{dt} \\a'(t) = k*(v(t)*v'(t)+v'(t)*v(t))\\a'(t) = 2k*v'(t)*v(t)[/tex]
