Question

In a relay race, runner A is carrying a baton and has a speed of 3.0 m/s . When he is 25M behind the starting line, runner B starts from rest and accelerates at .10 m/s^2. How long afterwards will A catch up with B to pass the baton to B?

Answer 1

distance covered by behind runner: 3*t

distance by starter: 1/2 a t^2

these times have to be equal,
so 3t-25=1/2(.1)t^2

multiply by 20, put in quadratic form
t^2-60t-500=0

t= (30-+ sqrt(3600/4 +500))

= 30 +- 10 sqrt (9+5)
now for an engneering check:
let sqrt (15) appx=4
t=70, or -10 throw out the negative time, we are not going backwards.
Distance covered by runner: 280
distance covered by starter: 4900*.05=appx 250 which sounds like a reasonable answer, as runner has to go 25 m further.

Work it accurately.