Question

An automobile starts from rest and travels down a straight section of road. The distance y (in feet) of the car from the starting position after x seconds is given by
y=f(x)=8x^2
(a) Find the instantaneous velocity at x=5 seconds (include units).
Instantaneous velocity =

(b) Find the instantaneous velocity at x=8 seconds (include units).
Instantaneous velocity =

Answer 1

instantaneous velocity is the first derivative of displacement.
\[v(x)={d\over dx}y(x)\\
v(x)={d\over dx}(8x^2)\\
v(x)=16x
\]

Answer 2

since "y" is in feet and "x" is in sec,
v(x) is measured in feet per sec.

for (a), x= 5
for (b) x=8