Grade 10
Course ContentKinematics
Habari Mwanafunzi! Welcome to the World of Kinematics!
Ever been in a matatu on the Thika Superhighway, feeling that push back into your seat as the driver accelerates? Or watched Ferdinand Omanyala explode out of the blocks in a 100m sprint? That's Kinematics in action! It's the branch of mechanics that describes how objects move, without worrying about why they move (we'll leave the 'why' for Dynamics, which involves forces).
In this lesson, we're going on a safari into the mathematics of motion. We'll learn to calculate speed, distance, and acceleration for everything from a boda-boda navigating Nairobi traffic to a mango falling from a tree. So, buckle up, this is where the math gets real and exciting!
The "Big Five": Key Quantities of Motion
Before we can start solving problems, we need to understand our main players. In Kinematics, we focus on five key quantities, often remembered by the acronym SUVAT.
- s - Displacement (in metres, m)
- u - Initial Velocity (in metres per second, m/s)
- v - Final Velocity (in metres per second, m/s)
- a - Acceleration (in metres per second squared, m/s²)
- t - Time (in seconds, s)
Distance vs. Displacement (s)
This is a crucial difference! Distance is the total path covered. Displacement is the straight-line distance from the start point to the end point, including direction.
Imagine you walk from the National Archives to Kencom House in Nairobi. You might have to walk along Moi Avenue and then turn, covering a distance of 300 metres. However, your displacement, the direct line between the two points, might only be 200 metres to the West. In vector mechanics, direction matters!
Image Suggestion: A stylized map of Nairobi CBD showing two points, like the GPO and the Hilton Hotel. One dotted line shows a winding path a person would walk (labeled 'Distance'). A second, straight arrow points from the start to the finish (labeled 'Displacement').
Velocity vs. Speed (u, v)
Similar to the above, Speed is how fast you're going. Velocity is your speed in a specific direction. So, 100 km/h is a speed. 100 km/h due North is a velocity.
Acceleration (a)
Acceleration is the rate at which your velocity changes. If your velocity is not changing, your acceleration is zero! When a matatu driver "steps on it", the vehicle accelerates. When they hit the brakes, the vehicle decelerates (which is just negative acceleration).
The Golden Rules: The SUVAT Equations of Motion
For any object moving with constant acceleration, we have a set of powerful equations. These are your best friends in Kinematics. You must know them by heart!
1. v = u + at (Doesn't involve displacement, s)
2. s = ut + ½at² (Doesn't involve final velocity, v)
3. v² = u² + 2as (Doesn't involve time, t)
4. s = ½(u + v)t (Doesn't involve acceleration, a)
Let's see them in action with a familiar scenario.
Example 1: The Matatu SprintA matatu, starting from rest at a bus stop, accelerates uniformly at 2 m/s² for 5 seconds. How far has it travelled and what is its final velocity?
Step 1: Identify your knowns and unknowns.
- It starts from rest, so u = 0 m/s.
- It accelerates at a = 2 m/s².
- The time taken is t = 5 s.
- We need to find the distance (displacement), s = ?
- We also need to find the final velocity, v = ?
Step 2: Choose the right equations.
To find the final velocity (v), we can use the equation that links u, a, t, and v. That's Equation 1!
v = u + at
v = 0 + (2)(5)
v = 10 m/s
To find the distance (s), we can use the equation that links u, a, t, and s. Equation 2 is perfect.
s = ut + ½at²
s = (0)(5) + ½(2)(5)²
s = 0 + 1 * 25
s = 25 m
Answer: The matatu reaches a velocity of 10 m/s and travels 25 metres in 5 seconds. Easy, right?
Vertical Motion: What Goes Up Must Come Down!
This is a special case of constant acceleration where the only force acting is gravity. We use the same SUVAT equations, but with one key change:
Acceleration 'a' is replaced by 'g', the acceleration due to gravity.
g ≈ 9.8 m/s² (We often use 10 m/s² for easier calculations in exams)
CRITICAL: You MUST define a direction as positive. A common convention is 'upwards is positive'. This means:
- Velocity of an object thrown up is positive.
- Velocity of a falling object is negative.
- Acceleration due to gravity (g) is always acting downwards, so it is always negative (a = -9.8 m/s²).
▲ +ve velocity (v)
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|
(Ball) a = -g (always downwards)
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▼ -ve velocity (v)
Example 2: The Falling MangoA ripe mango drops from a branch 5 metres above the ground. How long does it take to hit the ground, and with what velocity does it land?
Step 1: Identify your SUVAT values. (Let's take 'up' as positive)
- It drops, so the initial velocity is u = 0 m/s.
- The displacement is downwards, so s = -5 m.
- Acceleration is gravity, so a = -9.8 m/s².
- We need to find the time, t = ?
- We also need to find the final velocity, v = ?
Step 2: Choose your equations.
To find the final velocity (v), let's use the one without time (t). Equation 3!
v² = u² + 2as
v² = (0)² + 2(-9.8)(-5)
v² = 0 + 98
v = √98
v ≈ -9.9 m/s
(Note: We choose the negative root because the mango is moving downwards just before it hits the ground).
Now, to find the time (t), we can use the simplest equation. Equation 1.
v = u + at
-9.9 = 0 + (-9.8)t
-9.9 = -9.8t
t = -9.9 / -9.8
t ≈ 1.01 s
Answer: The mango hits the ground after about 1.01 seconds with a velocity of 9.9 m/s downwards.
Image Suggestion: A vibrant, photorealistic image of a lush green mango tree in a Kenyan shamba (farm). A single, ripe yellow-orange mango is captured mid-fall, with motion blur indicating its speed towards the ground below.
Visualising Motion: Displacement-Time & Velocity-Time Graphs
Graphs are a powerful way to see the story of an object's journey. For your STEM course, this also connects directly to Calculus!
Displacement-Time (s-t) Graphs
This graph shows an object's position over time.
- The gradient (slope) of the line gives you the velocity.
s | / s | ___ s | )
| / | / | /
| / | / | /
|_____/_____ t |____/______ t |___/_______ t
Constant Positive Object at Rest Increasing Velocity
Velocity (Gradient = 0) (Accelerating)
(v = ds/dt)
Velocity-Time (v-t) Graphs
This graph shows an object's velocity over time. These are even more useful!
- The gradient (slope) of the line gives you the acceleration (a = dv/dt).
- The area under the graph gives you the displacement (s = ∫v dt).
v |--------- v | / v | /
| | / | /
| | / | / Area = ½ * base * height
|___________ t |___/_______ t |___/_______ t
Constant Velocity Constant Positive Displacement is the
(Acceleration = 0) Acceleration Area of the Triangle
Example 3: Reading a GraphA sprinter's first 4 seconds are modelled by the v-t graph below. What is her acceleration and how far did she run?
v (m/s) | 10| / | / | / | / 5| / | / |/ --|----------- t (s) 0 2 4
Solution:
The graph is a straight line, so acceleration is constant. Acceleration = Gradient = (Change in v) / (Change in t) = (10 - 0) / (4 - 0) = 2.5 m/s².
The distance covered is the area under the graph. The shape is a triangle. Displacement = Area = ½ * base * height = ½ * 4 * 10 = 20 metres.
You've Got This!
Kinematics is like a puzzle. You are given some pieces of information (s, u, v, a, t), and you have to use the right equations and logic to find the missing ones. Practice is key! Work through the examples in your textbook, try to create your own scenarios, and you'll become a master of motion in no time.
This is the foundation for almost everything else in mechanics and physics. Understanding it well will open doors to understanding planetary orbits, designing machines, and so much more. Keep up the great work!
Pro Tip
Take your own short notes while going through the topics.
