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.


f. When was the rocket’s acceleration greatest?

Verified step by step guidance

1. To determine when the rocket's acceleration was greatest, we need to analyze the velocity-time graph provided.
2. Acceleration is the rate of change of velocity with respect to time. Mathematically, it is the derivative of the velocity function with respect to time.
3. On a velocity-time graph, the acceleration is represented by the slope of the tangent to the curve at any given point.
4. Identify the section of the graph where the slope is steepest. This indicates the greatest change in velocity over the shortest period of time, which corresponds to the greatest acceleration.
5. From the graph, observe that the steepest slope occurs at the beginning of the flight, just after launch, indicating that the rocket's acceleration was greatest during the initial phase of the propellant burn.

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's flight, 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 determined from the slope of the velocity graph; a steeper slope indicates greater acceleration. In the rocket's flight, acceleration is greatest when the velocity is changing most rapidly, which occurs during the initial launch and when the rocket is descending.

Graph Interpretation

Interpreting graphs involves analyzing the visual representation of data to extract meaningful information. In this case, understanding the velocity vs. time graph allows us to identify key moments in the rocket's flight, such as when it accelerates, reaches its peak velocity, and begins to decelerate, which is crucial for answering questions about the rocket's motion.