A car speeds, at a constant 16 m/s, past a parked police motorcycle. Five seconds later, the police officer leaves on her motorcycle, and accelerates at 2 m/s2. How many seconds until she catches the car?
x = 16 t
also
x = (1/2)(2) (t-5)^2
so
16 t = t^2 - 10 t + 25
t^2 - 26 t + 25 = 0
t = [ 26 +/- sqrt(676-100) ]/2
t = [ 26 +/- 24 ]/2
t = 2 or t = 25
t = 2 is negative x at start so use t = 25
which is 400 meters from start