Successive Posts Revision Notes for Leaving Cert Applied Maths

Successive Posts

What are successive posts problems?

Successive posts problems involve objects moving with constant acceleration past a series of fixed points (posts) along a straight path. These problems require you to use information about the distances between posts and the time taken to travel between them to find unknown values like acceleration or initial velocity.

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The key insight is that you can analyse both individual sections of the journey and the complete journey from start to finish, then use these different perspectives to create simultaneous equations.

Key approach and method

When tackling successive posts problems, follow this systematic approach:

Draw a clear diagram showing the posts, distances between them, and time intervals
Identify what you know and what you need to find
Apply kinematic equations to different sections of the journey
Set up simultaneous equations using the relationships you've found
Solve the equations to find the unknown values

Essential kinematic equation

The most useful equation for these problems is:

$s = ut + \frac{1}{2}at^2$

Where:

s = displacement (distance travelled)
u = initial velocity
a = acceleration (constant)
t = time taken

Worked example: Car passing three posts

Let's examine a typical successive posts problem to understand the method clearly.

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Worked Example: Finding Acceleration

Problem: A car moving with constant acceleration passes three posts A, B, and C on a straight road. The distance from A to B is 48 m, and from B to C is 102 m. The car takes 4 seconds to travel from A to B, and 6 seconds to travel from B to C. Find the car's acceleration.

Step-by-step solution

Step 1: Draw and label a diagram

A -------- B -------- C
   48 m      102 m
   4 s       6 s

Step 2: Define variables

Let u = initial velocity as the car passes post A
Let a = acceleration of the car

Step 3: Apply the kinematic equation to the first section (A to B)

For the journey from A to B:

Initial velocity = $u$
Time = 4 s
Distance = 48 m
Acceleration = $a$

Using $s = ut + \frac{1}{2}at^2$ :

$48 = u(4) + \frac{1}{2}(a)(4)^2$

$48 = 4u + 8a$

$12 = u + 2a$ ... (Equation 1)

Step 4: Apply the kinematic equation to the complete journey (A to C)

For the entire journey from A to C:

Initial velocity = $u$ (same as before)
Time = $4 + 6 = 10$ s
Distance = $48 + 102 = 150$ m
Acceleration = $a$

Using $s = ut + \frac{1}{2}at^2$ :

$150 = u(10) + \frac{1}{2}(a)(10)^2$

$150 = 10u + 50a$

$15 = u + 5a$ ... (Equation 2)

Step 5: Solve the simultaneous equations

From Equation 1: $u + 2a = 12$ From Equation 2: $u + 5a = 15$

Subtracting Equation 1 from Equation 2: $(u + 5a) - (u + 2a) = 15 - 12$

$3a = 3$

a = 1 m/s²

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Important Tips for Success

Always draw a diagram - this helps visualise the problem and prevents mistakes
Consider both individual sections and the complete journey - this gives you the different equations needed
Check your units - make sure all measurements are in consistent units (metres and seconds)
Show your working clearly - partial marks are often available even if your final answer is incorrect

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Alternative Approaches

You could also solve these problems using:

Average speed calculations for quicker solutions in some cases
The equation $v = u + at$ if you need to find velocities at specific points
Graphical methods using velocity-time graphs

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Key Points to Remember:

Successive posts problems involve objects with constant acceleration passing multiple fixed points
Draw a clear diagram showing distances and time intervals to organise your information
Use $s = ut + \frac{1}{2}at^2$ applied to both individual sections and the complete journey
Set up simultaneous equations from the different sections to solve for unknowns
Always check your units and show clear working for maximum marks

Successive Posts (Leaving Cert Applied Maths): Revision Notes