A train is at rest at a station. The train then moves away from the station and after 20 seconds it's velocity is 15m/s and moves at this velocity for 60 seconds. it's velocity increases to 20m/s over 5 seconds. it moves at a velocity of 20m/s for 120 seconds and then slows down to come to a stop after a further 30 seconds. during which period was the acceleration of the train the highest?

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Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.