**Problem 1C-06*:** Addition of velocity and acceleration vectors

(a) A train is moving in a flat plane with a velocity vector **v** at certain
moment as shown in Fig.1. A coin located at point P on the rough floor of the
train is sliding with a velocity **u** relative to the train at that moment.
From the view of a ground observer, what is the velocity vector of the coin?

(b) Suppose that the train is entering a curve at that moment and has an
acceleration vector **a** as shown in Fig.1. On the other hand the coin is
experiencing a deceleration that has a magnitude b and is antiparallel to
**u**. What is the acceleration vector of the coin observed by the ground
observer?

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**Solution:**

(a) Since the point of P of the floor is moving along with the train, it
has a velocity vector **w** that is parallel to **u**, has the same
magnitude as the magnitude of **u**, and originates from point P. The floor
is rough, so the coin is pulled by point P and inherits the same velocity
vector **w**. The velocity vector **w** of the coin can be summed with
the velocity vector **u** of the coin and results in the velocity vector
**w**+**u** that the ground observer observes as shown in Fig.2

(b) The same argument as part (a) indicates that the coin inherits an acceleration
vector **A** that is parallel to **a**, has the same magnitude as the
magnitude of **a**, and originates from the coin at point P at the moment of
concern. The deceleration vactor of the coin, denoted as **b**, that also
originates from the coin at point P is

Make sure that the vector

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