Apply Newton's Law: F = ma = m(dv/dt) where m = 2000 kg, vo = 20 meters/sec, t = time (sec)
in this problem, F = -2000 newtons (kg*m/sec^2), So, (2000 kg)(dv/dt) = 2000 newtons or
dv/dt = -1 m/sec^2 and dv = -1 dt. Integrating, we find that v = -t + constant,
the constant is 20 m/sec (vo) at t = 0. and the velocity equation is v = -t + 20
from this equation, when v=0 or when the car stops, time = 20 seconds.
But v = dx/dt -t + 20 where x is the distance traveled. Integrating, we get
x = (-.5)t^2 + 20t + constant at t=0, x = 0, this constant is zero. that leaves
x = (-.5)t^2 + 20t but we know that the car stops at 20 seconds, that tells us that
x = (-.5)(20^2) + 20(20) = 200 seconds.
