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...

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.