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Master the math behind changing speeds and understand the units of acceleration.
What if you could tell exactly how powerful a supercar is just by looking at a stopwatch? Acceleration is the secret language of motion that tells us how quickly things change.
In everyday talk, we use 'acceleration' to mean speeding up. But in Physics, acceleration is defined as the rate at which an object changes its velocity. Because velocity includes both speed and direction, you are accelerating if you speed up, slow down, or even change direction! If you are riding a bike and you pedal harder to go faster, you are accelerating. If you pull the brakes to slow down for a red light, you are also accelerating (just in a negative direction).
Quick Check
If a car travels at a perfectly steady 60 mph in a straight line, is its acceleration zero or positive?
Answer
Zero, because the velocity is not changing.
A sprinter starts from rest () and reaches a velocity of in seconds. What is their acceleration?
1. Identify the variables: , , . 2. Set up the formula: . 3. Calculate the result: .
Quick Check
What does the unit actually represent?
Answer
It represents the change in velocity (meters per second) per second of time.
When an object slows down, its final velocity is smaller than its initial velocity. When you plug these numbers into the formula, you will get a negative result. In physics, a negative acceleration value usually indicates that the object is slowing down, which we often call deceleration. For example, if a car goes from to , the change () is . This negative sign is crucial because it tells us the direction of the acceleration is opposite to the motion.
A skateboarder rolling at sees a curb and brakes to a complete stop in seconds. Calculate the acceleration.
1. Identify the variables: , (stop), . 2. Set up the formula: . 3. Calculate the result: .
Sometimes we need to find acceleration during a specific window of time. Imagine a rocket already moving at high speed that ignites a secondary booster. To find the acceleration, we don't care about the rocket's history from ; we only care about the velocity at the start of the timing and the velocity at the end of the timing. This allows us to calculate acceleration at any point in a journey.
A truck is cruising at . To pass a slow car, it speeds up to . If this speed increase takes seconds, and then the truck maintains that for another seconds, what was the acceleration during the 5-second speed-up phase?
1. Focus only on the change phase: , , . 2. Ignore the 'extra' 10 seconds as the speed isn't changing then. 3. Apply formula: . 4. Result: .
Which of the following is the correct unit for acceleration?
A car accelerates from to in seconds. What is its acceleration?
In physics, acceleration only refers to an object speeding up.
Review Tomorrow
In 24 hours, try to write down the acceleration formula from memory and explain what each letter () stands for.
Practice Activity
Next time you are in a car, watch the speedometer. If the car goes from 0 to 60 km/h, try to count how many seconds it takes and estimate the acceleration!