# What is the acceleration?  A person running in a moving train accelerates at 1 m/s. What is the acceleration of the person as measured by someone standing on the station, if the train is moving...

What is the acceleration?

A person running in a moving train accelerates at 1 m/s. What is the acceleration of the person as measured by someone standing on the station, if the train is moving at 60 km/h?

justaguide | College Teacher | (Level 2) Distinguished Educator

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Let us assume the person standing on the station measures the velocity of the person running on the train at two instances of time t1 and t2 to calculate the acceleration. If the person has a velocity v1 with respect to the train at time t1 and a velocity v2 with respect to the train at t2, the person on the station measures the velocity at t1 as v1 + 60*1000/3600 m/s and at t2 as v2 + 60*1000/3600 m/s.

Now v2 = v1 + acceleration* time for the person running with respect to the train.

=> v2 = v1 + 1*(t2 – t1)

The observer sees that v2 + 60*1000/3600 = v1 + 60*1000/3600 + 1*(t2 – t1)

we can cancel 60*1000/3600

=> v2 = v1 + 1*(t2 – t1)

Therefore the observer also measures an acceleration of 1 m/s^2.