Question

Please help! :)

When a car's brakes are applied, the speed of the car is given by v(t) = 80 - 22t (in ft per second). Use the area under the function to determine how many feet the car travels between the time the brakes are applied (t = 0) and the time the car stops.

Answer 1

can you draw more or less the function v(t) and show that area?

Answer 2

v(t) = 80 - 22t. t = 0
v(0) = 80 - 22(0)
v0=80-0
so I wonder is the answer 80 ft per second

Answer 3

that is, determine the value
\[I=\int_0^T v(t)\,dt\] where \(T\) is the number such that \(v(T)=0\).
we get \(T=80/22=40/11\).
Therefore, \(I=\int_0^{T}v(t)\,dt = [80t- 11t^2]^T_0 = \dots\)