Remember that the speed is the rate of change of the position with respect to time, so to solve this we are going to use the kinematic equation: [tex]S= \frac{d_{f}-d_{i}}{t_{f}-t_{i}} [/tex]
where
[tex]S[/tex] is the speed of the train
[tex]d_{i}[/tex] is the initial distance
[tex]d_{f}[/tex] is the final distance
[tex]t_{i}[/tex] is the initial time
[tex]t_{f}[/tex] is the final time
Since checkpoint A is the initial checkpoint, we can infer that [tex]d_{i}=105[/tex] and [tex]t_{i}=2[/tex]. Similarly, since checkpoint B is the final checkpoint, we can infer that [tex]d_{f}=285[/tex] and [tex]t_{f}=5[/tex]. Lets replace the values in our kinematic euation:
[tex]S= \frac{d_{f}-d_{i}}{t_{f}-t_{i}} [/tex]
[tex]S= \frac{285-105}{5-2} [/tex]
[tex]S= \frac{180}{3} [/tex]
[tex]S=60[/tex] mph
We can conclude that the train's speed between checkpoints is 60 mph.
