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​(a) How fast was the rocket climbing when the engine​ stopped?

To determine the speed of the rocket when the engine stopped, we need to identify the time when the engine burned out. The engine typically burns out right before the velocity stops increasing.

Looking at the velocity-time graph, the velocity increases up to a peak value at around \( t = 3 \, \text{seconds} \), after which the velocity starts to decrease. This peak corresponds to the time when the engine stops, and the rocket starts to coast upward without thrust.

From the graph, at \( t = 3 \, \text{seconds} \), the velocity is approximately 180 feet per second (ft/sec).

Thus, the rocket was climbing at **180 ft/sec** when the engine stopped.

Would you like any further clarification or details?

Here are 5 related questions to expand on the topic:

1. What happens to the rocket's velocity after the engine burns out?
2. How can we calculate the rocket's maximum altitude from this graph?
3. What is the significance of the time when the velocity becomes negative?
4. Can you explain how the parachute affects the velocity after deployment?
5. What role does gravity play in the rocket's deceleration after engine burnout?

**Tip:** Always look for the peak in a velocity-time graph to determine when an object stops accelerating, as it marks a change from powered flight to coasting or deceleration.

(a) How fast was the rocket climbing when the engine stopped?

Learn how to determine the speed of a model rocket when its engine burns out using a velocity-time graph. This problem involves interpreting the peak of the graph and analyzing kinematics concepts. Suitable for Grades 9-12 physics students.

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