Question

6. A subway train is travelling at 80km/h when it approaches a slower train 50 m ahead
travelling in the same direction at 25 km/h. if the faster train begins to decelerate at 2.6
m/s²
. While the slower train continues at constant speed. How soon and what relative
speed will they collide.

Answer 1

$V_1=80\;km/h=80\frac{1000}{3600}=22.22 \;m/s.$

$V_2=25\;km/h=25\frac{1000}{3600}=6.94 \;m/s.$

$V_2t+50=V_1t-\frac{at^2}{2}$ .

$6.94t+50=22.22t-\frac{2.6t^2}{2}.$

$1.3t^2-15.28t+50=0.$

This equation does not have real roots.

Therefore, the trains never collide.