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### 304-M: Kinematic Equations 9B: Velocity to other graphs in two directions

• Topic Cluster: Kinematics
• Topic: Forward and Backwards Kinematics Quantitative
• Objective: Given a velocity-time graph of an object moving in two different directions, draw a corresponding position-time graph and acceleration-time graph; includes only constant acceleration motion
• Content:
• Level: 4

#### BACK to Ladder Forward and Backwards Kinematics Quantitative

A spaceship on planet Zeryon is flying eastward into enemy territoy at a speed of 500 m/s, when a warlock creates a force field around the planet. Heretofore, the spaceship experiences constant acceleration of 2 m/s/s westward. The truly incompetant helmsman does not change course for five minutes.

1. Draw a quantitative velocity-time graph for the ship from $$t = 0$$ to $$t = 5 \text{ min}$$.
2. Indicate on your graph explicitly where the ship reverses direction.
3. Determine how far the ship travels before reversing direction.
4. Determine the time before the ship is back where it started. Indicate this time clearly on your graph.
5. Determine the final displacement of the plane.
6. On your velocity-time graph, indicate three different areas as A, B, and C:
1. In Area A, the ship is moving eastwards.
2. In Area B, the ship is moving westwards, but is still east of its initial position.
3. In Area C, the ship is moving westwards and is west of its initial position.
4. Demonstrate quantitatively that Area A = Area B. By referring to the fundamental theorem of calculus as listed above, explain why this must be the case.
5. From a kinematic equation, determine the total displacement of the ship after five minutes. (This should be already completed.) Demonstrate quantitatively that Area C = the toatl displacement of the plane after five minutes.