**Particle Moving Along a Straight Line**

To solve this problem, we need to consider a particle moving along a straight line with a constant velocity Voj. We are given that the particle is at the position (a,0) at t=0. Our goal is to find the velocity of the particle, vr, at a given time t.

**Understanding the Problem**

Before we begin, let's understand the problem in more detail. We have a particle moving along a straight line, which means its motion is only in one dimension. The position of the particle is given by the coordinate x=a, where a is a constant. This means that the particle is always at a fixed distance 'a' from the origin in the x-direction.

**Velocity of the Particle**

The velocity of a particle is defined as the rate of change of its position with respect to time. In this case, since the velocity is constant, we can say that the particle covers equal distances in equal intervals of time. Therefore, the velocity can be represented as Voj = Δx/Δt, where Δx is the change in position and Δt is the change in time.

**Determining the Velocity at a Given Time**

To find the velocity of the particle at a given time t, we need to determine the change in position Δx and the change in time Δt. Since the particle is at the position (a,0) at t=0, the initial position x0=a and the initial time t0=0.

Let's assume that at time t, the particle has moved to a new position x. Therefore, the change in position Δx can be calculated as Δx = x - x0 = x - a.

Similarly, the change in time Δt can be calculated as Δt = t - t0 = t - 0 = t.

Now, substituting these values in the equation for velocity Voj = Δx/Δt, we get:

Voj = (x - a)/t

**Conclusion**

In conclusion, the velocity of the particle at a given time t can be calculated using the equation Voj = (x - a)/t, where x is the position of the particle at time t and a is the initial position of the particle. This equation gives us the rate of change of position with respect to time, allowing us to determine the velocity of the particle at any given time.