Question

A car traveling 96ft/s begins a negative acceleration at a constant rate of 12ft/s^2. After how many seconds does the car come to a stop? How far will the car have traveled before stopping? Anti-derivatives are involved somewhere in the 2nd part I believe.

Answer 1

vf^2=Vi^2+2ad

a=-12, vf=0, solve for d (in feet): now with integrals...

vf=vi+at
int vf*dt=Int vi*dt + INT atdt
distance=vi*t+1/2 a t^2
but you need time first...
vf=vi+at
0=96-12t solve for time t.