**Problem 1C-02*:** Velocity and acceleration vectors of a straight line motion

The motion of a particle in a flat plane is described as

x(t)=At+B,

and
with A ≠ 0 and C ≠ 0
(1)

y(t)=Ct+D.

Use the concepts of velocity vector and acceleration vector to describe the motion.

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**Solution:**

Let the velocity vector be denoted in the rectangular coordinate representation as

**v**(t) = (v_{x}(t), v_{y}(t))

and the acceleration vector as

**a**(t) = (a_{x}(t), a_{y}(t)).

Since from Eqs.(1) we have

the velocity vector

Thus the particle starts from the point (B, D) at t = 0, and moves along the trajectory with a constant speed |

For the acceleration vector

This means that there is no acceleration for the motion so that the velocity of the particle does not vary; the direction and the magnitude of the velocity vector are both independent of time, just as we have found earlier.

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