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Learn to read graphs that show how an object's speed changes over time.
Imagine you are a race car engineer looking at a data screen. Without seeing the track, how could you tell if your driver just hit the brakes or is flooring the gas pedal just by looking at one single line?
In a velocity-time (v-t) graph, we plot time () on the horizontal x-axis and velocity () on the vertical y-axis. Unlike a distance-time graph, which shows where an object is, a v-t graph shows how fast it is moving at any exact moment. If the line is at a high point on the y-axis, the object is moving fast. If the line is at zero, the object has stopped. A horizontal line doesn't mean the object isn't moving; it means the velocity is constant (not changing).
Quick Check
If a velocity-time graph shows a flat, horizontal line at , is the object moving?
Answer
Yes, it is moving at a steady speed of .
A cyclist starts from rest () and reaches a velocity of in . 1. Identify the change in velocity: . 2. Identify the change in time: . 3. Calculate slope: .
Quick Check
What does a steeper line on a velocity-time graph tell you about the object's acceleration?
Answer
It indicates a higher or greater acceleration.
We can tell the direction of acceleration by looking at the direction of the line. If the line is moving away from the zero line (the x-axis), the object is speeding up. This is a positive acceleration. If the line is moving toward the zero line, the object is slowing down (also called deceleration or negative acceleration). Even if the line is still 'high' on the graph, if it is pointing downwards, the object is losing speed.
A car is traveling at . The driver sees a red light and slows to over . 1. Initial velocity () = , Final velocity () = . 2. . 3. . 4. On the graph, this would be a line starting at and sloping down to the x-axis.
Imagine a rocket: 1. It accelerates from to in (Steep upward line). 2. It stays at for (Horizontal line). 3. It runs out of fuel and slows to in (Long, gentle downward line). To find the total behavior, you must analyze each segment's slope separately.
On a velocity-time graph, what does a horizontal line at represent?
If the slope of a v-t graph is negative (pointing down), the object is:
A straight diagonal line on a v-t graph represents constant acceleration.
Review Tomorrow
In 24 hours, try to sketch three v-t graphs: one for a car at a stoplight, one for a car accelerating, and one for a car cruising on a highway.
Practice Activity
Look at a graph of a sprinter. Calculate their acceleration for the first 2 seconds if they go from to .