Answer:
[tex]-0.16 m/s^2[/tex]
Explanation:
First of all, we need to calculate the distance covered by the locomotive during the reaction time. This is given by
[tex]d_1 = u t_1[/tex]
where
u = 11 m/s is the initial velocity of the locomotive
[tex]t_1=0.43 s[/tex] is the reaction time
Substituting,
[tex]d_1 = (11)(0.43)=4.7 m[/tex]
So the distance left between the locomotive and the car is
[tex]d=380-4.7 =375.3 m[/tex]
Now we can find the minimum deceleration to avoid the accident with the equation
[tex]v^2-u^2=2ad[/tex]
where
v = 0 is the final velocity
u = 11 m/s
a is the deceleration
d = 375.3 m is the stopping distance
Solving for a,
[tex]a=\frac{v^2-u^2}{2d}=\frac{0-11^2}{2(375.3)}=-0.16 m/s^2[/tex]
