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The problem you've provided describes a particle moving with uniform acceleration from rest. Let's break it down step-by-step:

### Given:
1. The particle starts from rest at point \( O \).
2. It passes through points \( P \), \( Q \), and \( R \).
3. Distances: 
   - \( |PQ| = 105 \, \text{m} \)
   - \( |QR| = 63 \, \text{m} \)
4. Time:
   - The time taken to travel from \( P \) to \( Q \) is 6 seconds.
   - The time taken to travel from \( Q \) to \( R \) is 2 seconds.
   
We are asked to **calculate the acceleration of the particle**.

### Approach:
We'll use the equations of motion under constant acceleration. The first step is to apply the kinematic equation:
\[
s = ut + \frac{1}{2} a t^2
\]
where:
- \( s \) is the displacement,
- \( u \) is the initial velocity,
- \( t \) is the time, and
- \( a \) is the acceleration.

#### Step 1: Motion from \( P \) to \( Q \)
- Distance: \( PQ = 105 \, \text{m} \),
- Time: \( t_{PQ} = 6 \, \text{seconds} \).

Since the particle moves with uniform acceleration from rest:
- The velocity at \( P \) is unknown, but we can use the equation:
\[
PQ = u_P \cdot t_{PQ} + \frac{1}{2} a t_{PQ}^2
\]
Since \( u_P \) is the velocity at point \( P \), we need to calculate this using another relationship from \( Q \).

Let me calculate the acceleration for you using these relationships.The acceleration of the particle is approximately \( 5.83 \, \text{m/s}^2 \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How do we calculate the velocity at point \( Q \)?
2. How would we calculate the velocity of the particle at point \( R \)?
3. What is the total distance traveled by the particle from \( O \) to \( R \)?
4. How does uniform acceleration affect the time intervals between points?
5. Could we calculate the time it takes to reach point \( P \) from rest?

**Tip:** When dealing with uniform acceleration, kinematic equations are essential tools for connecting displacement, velocity, time, and acceleration.

A particle starts at point O from rest and moves in a straight line with uniform acceleration. It passes three points, P, Q, and R, with |PQ| = 105 m and |QR| = 63 m. It takes 6 seconds to travel from P to Q and 2 seconds to travel from Q to R. (a) Calculate the acceleration of the particle.

In this problem, a particle moves from rest with uniform acceleration through points P, Q, and R. Learn how to calculate the particle's acceleration using kinematic equations with given distances and times. Ideal for students in Grades 11-12 studying motion in physics.

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