Understanding Motion from Graphs


Launching a Rocket When a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for a while and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the rocket to keep it from breaking when it lands.


The figure here shows velocity data from the flight of the model rocket. Use the data to answer the following.


a. How fast was the rocket climbing when the engine stopped?

Verified step by step guidance

1. Examine the graph provided, which plots velocity (in ft/sec) against time (in seconds) for the model rocket's flight.
2. Identify the point on the graph where the rocket's engine stops burning. This is typically where the velocity reaches its maximum before starting to decrease.
3. Observe the peak of the graph, which represents the maximum velocity achieved by the rocket during the engine burn phase.
4. Determine the time at which this peak occurs by looking at the x-axis. This is the moment when the engine stops and the rocket begins to coast.
5. Read the corresponding velocity value at this peak from the y-axis. This value is the speed at which the rocket was climbing when the engine stopped.

Key Concepts

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both speed and direction. In the context of the rocket launch, the velocity graph shows how fast the rocket is moving at different times, indicating periods of ascent, coasting, and descent.

Acceleration

Acceleration is the rate of change of velocity over time. It can be positive (speeding up) or negative (slowing down). In the rocket's flight, acceleration occurs during the burn phase when the engine is active, and it changes as the rocket coasts and then falls, which can be inferred from the slope of the velocity graph.

Graph Interpretation

Interpreting graphs involves analyzing the visual representation of data to extract meaningful information. In this case, the velocity vs. time graph allows us to determine key moments in the rocket's flight, such as when the engine stops and the maximum height reached, by observing the changes in the graph's slope and direction.