In this question, position vectors are given relative to a fixed origin - Edexcel - A-Level Maths Mechanics - Question 1 - 2022 - Paper 1

The acceleration a of particle P is the derivative of the velocity v with respect to time t. Since the given velocity is:

$$v = 3i - 6j$$

Differentiating with respect to t gives:

a = rac{dv}{dt} = 0i + 0j = 0 ext{ m/s}^2.

Thus, the acceleration is zero, indicating constant velocity.

To find the position vector r at time t = 1 second, we integrate the velocity vector with respect to time, considering the initial position vector at t = 0 as the constant of integration:

$$ext{r} = ext{r}_0 + ext{v} imes t$$

Using the known velocity of v and integrating:

At t = 1:

$$ext{r} = ext{r}_0 + (3i - 6j)\times1 = ext{r}_0 + 3i - 6j.$$

Since we need the position at t = 1 second and assume the initial position at t = 0 is (0i + 0j), we have:

$$ext{r} = 3i - 6j.$$