I have a question on one of the physics problems. A train moves forward at a con

Question

I have a question on one of the physics problems.

A train moves forward at a constant speed of 15.0m/s for 10.0 min and then accelerates at a constant rate for 8.00 min, eventually reaching a final forward speed of 25.0 m/s. Which one of the following choices best describes how far the train traveled during this evtire 18.0 min process?

So I tried solving the problem and got 9000m when the speed was 15m/s for 10 min but then when it accelerates and reaches 25m/s I got 12000m. Thus, the total distance would be 21000m but the answer was 18600m. From where did I make a mistake?

Explanation / Answer

in the 1st part of the journey you are right the train travels 15*600=9000m

but in the 2nd part the train accelerates for 8min=480s

So acceleration = (25-15)/480 = 1/48 m/s^2

so the distance travelled will be S=ut+(1/2)at^2

u=15m/s t=480s a=1/48 m/s^2

you get S=9600m

So the total distance would be 9000+9600=18600m

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