Question

A subway train starts from rest at a station and accelerates at a rate of 1.6 m/s2 for 14 s. It runs at constant speed for 70 s and slows down at a rate of 3.5 m/s2 until it stops at the next station. Find the total distance covered in meters

Answer 1

The total distance covered by a subway

$$d=d_1+d_2+d_3$$

Here

$$d_1=\frac{a_1t_1^2}{2}=\frac{1.6\times 14^2}{2}=1568\:\rm m$$

$$d_2=v_2t_2=(a_1t_1)t_2=1.6\times 14\times 70=1568\:\rm m$$

$$t_3=v_2/a_3=1.6\times 14/3.5=6.4\:\rm s$$

$$d_3=\frac{v_2+0}{2}t_3=\frac{1.6\times 14+0}{2}\times 6.4=71.68\:\rm m$$

Finally

$$d=1568+1568+71.68=3207.68\:\rm m$$