Rectilinear acceleration

Acceleration simply means how quickly something speeds up, slows down, or changes direction in a straight line. When a vehicle increases its speed, that's positive acceleration. When it applies brakes and slows down, that's negative acceleration, also called deceleration. Think of a commercial bus accelerating from rest at a Lagos traffic light—as it speeds up, the passengers feel pushed backward. That's acceleration in action.

The key thing to understand is that acceleration measures the rate of change of velocity over time. If a car's speed changes from 10 m/s to 20 m/s in 2 seconds while moving in one direction, we calculate acceleration as the change in velocity divided by time. Both speeding up and slowing down count as acceleration because velocity is changing in both cases.

Acceleration simply means how quickly something's speed changes. When acceleration is uniform, the speed increases or decreases by the same amount every second. Think of a car moving on a straight Lagos-Ibadan expressway at constant traffic flow—if it increases speed by 2 m/s every second, that's uniform acceleration.

Non-uniform acceleration happens when the speed change is irregular. Imagine a danfo bus in Lagos traffic. It might speed up 5 m/s in one second when the road clears, then only 1 m/s the next second when traffic builds up again. The acceleration keeps changing.

The key difference: uniform acceleration has constant rate of change, while non-uniform acceleration does not. You can use straight-line graphs for uniform acceleration but curved graphs for non-uniform cases.

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A velocity-time graph shows how an object's speed changes over time. The horizontal axis represents time while the vertical axis shows velocity. When you plot this graph, the shape tells you everything about the motion.

If the line is straight and horizontal, the object moves at constant velocity—no acceleration. When the line slopes upward, the object is accelerating (speeding up), and a downward slope means deceleration (slowing down). The steeper the slope, the greater the acceleration.

Consider a Lagos danfo bus starting from a traffic light. At first it accelerates rapidly, so the graph line slopes steeply upward. As it reaches cruising speed on the expressway, the line becomes horizontal. Then approaching the next bus stop, the line slopes downward as the driver brakes.

The area under the velocity-time graph represents the total distance covered—this is crucial for solving problems. A triangular area means different distance than a rectangular area under the same time period.

When an object moves in a straight line and its speed changes at a steady rate, we say it has constant acceleration. The equations of motion help us calculate distance, velocity, and time without needing complicated calculus.

The three main equations are: v = u + at, s = ut + ½at², and v² = u² + 2as. Think of a danfo bus accelerating smoothly from Lekki to Victoria Island—if it increases speed uniformly, you can predict exactly where it'll be after five seconds.

Motion under gravity is simply constant acceleration in action. When you drop something from a height, it accelerates downward at 9.8 m/s² (we call this g). This makes gravity problems easier because we already know the acceleration value.

The key is identifying what you know and what you're looking for, then choosing the right equation.