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:

1. Draw a tangent line at the 5-second mark.
2. Calculate the gradient of the tangent line.
3. 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.