Question

You are going to Chicago for the weekend and you decide to go by taking the train. Unfortunately, you are late for finishing your math exam, so you arrive late at the train station. You run as fast as you can, but just as you reach the platform your train departs, 30 meters ahead of you down the platform. You can run at a maximum speed of 8 m/s and the train is accelerating at 0.8 m/s². You can run along with the platform for 50 meters before a barrier prevents you from going further. Will you catch the train on time?

Answer 1

The given Values

V_y=your speed=8 m/s

X_t=Initial position of the train=30m

a_t=accelaration of the train =.08m/s²

X_p=length of the platform =50 mtr

The motion of the train can be descirbed by

X=X_t+ 1/2 at² ----------(1)

Your motion can be descibed by

X=V_y*t

t= X/V_y ----- (2)

equation (2) substitiute in equ (1)

now we get X=X_t+ 1/2 a *( X / V_y)²

re write the equation in the form of quadratic equation

X=( a / V_y² ) * (x²-x+X_t)

the quadratic equation X= (-b +/- sqrt (b²-4ac))/2 * a

X= (1 +/- sqrt ( -1²- 4* 1/2 * a *( X / V_y)² *X_t)/ 2 * 1/2 * a *( X / V_y)²

Substitute the values in this equation the we will get

X= ((1 +/- sqrt ( -1²- 4* 1/2 *(0.08m/s² )* 8 m/s *30 m ) /( 2 *1/2 *(0.08m/s² )* 8 m/s)

now we get two values in X =40m or x=120m

so you will catch the train after 5 seconds at 40m from your starting position.