Question

# At a distance ( L=400 mathrm{m} ) from the traffic light, brakes are applied to a locomotive moving at a velocity ( v=54 mathrm{km} / mathrm{hr} . ) Determine the position of the locomotive relative to the traffic light 1 minute after the application of the brakes if its acceleration is ( -0.3 mathrm{m} / mathrm{sec}^{2} ).

Solution

( u=54 times frac{5}{18}=15 mathrm{m} / mathrm{s} )

( a=-0.3 mathrm{m} / mathrm{s}^{2} )

( therefore quad v=u+a t )

( 0=15-0.3 mathrm{t}_{0} )

( t_{0}=frac{15}{0.3}=50 mathrm{sec} )

After 50 second, locomotive comes in rest permanently. ( therefore quad v^{2}=u^{2}+2 a s )

[

begin{array}{l}

mathrm{O}^{2}=15^{2}-2 times 0.3 mathrm{S}_{0}

mathrm{S}_{0}=frac{225}{0.6}=frac{2250}{6}=375 mathrm{m}

end{array}

]

the distance of the locomotive from traffic light ( =400-375=25 cdot mathrm{metre} )