Curvy Velocity-Time Graphs
Curvy velocity-time graphs represent more complex motion patterns where acceleration is not constant. These graphs require careful analysis to extract meaningful information about an object's motion.
Definition: A velocity-time graph shows how an object's velocity changes over time. The shape of the curve indicates the type of motion and acceleration experienced by the object.
Calculating Acceleration from a Curved Velocity-Time Graph
To find the acceleration at a specific point on a curved velocity-time graph, we need to determine the gradient of the tangent line at that point.
Example: To find the acceleration at 5 seconds:
- Draw a tangent line at the 5-second mark.
- Calculate the gradient of the tangent line.
- The gradient represents the acceleration at that point.
In the given example, the acceleration at 5 seconds is calculated as follows:
Acceleration = 22−8 / 10−5 = 2.75 m/s²
Highlight: The acceleration at any point on a curved velocity-time graph is equal to the gradient of the tangent line at that point.
Estimating Total Distance Traveled
To estimate the total distance traveled from a velocity-time graph, we calculate the area under the curve.
Example: The total distance traveled is estimated by dividing the area under the curve into shapes and summing their areas:
50 + 125 + 175 + 175 + 125 + 50 = 700 metres
Vocabulary: Area under velocity-time graph represents the total distance traveled by an object during the time interval shown on the graph.
