Graphical Differentiation
Position x (m) vs time t (s) graph of a particle is a parabola opening upward: x = 2 + 3t + t². Find velocity at t = 4 s.
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About This Question
- Subject
- physics
- Chapter
- kinematics
- Topic
- graphical differentiation
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
11 m/s
- Relationship: Instantaneous velocity is the time derivative of the position function: v(t)=dtdx.
- Differentiate: For x(t)=2+3t+t2:
- dtd(2)=0
- dtd(3t)=3
- dtd(t2)=2t
- Isolate v: v(t)=3+2t.
- Evaluate at point: For t=4 s:
- v(4)=3+2(4)=3+8=11 m/s.
- Result: The velocity at 4 seconds is 11 m/s.
This medium difficulty physics question is from the chapter kinematics, covering the topic of graphical differentiation. It appeared in the 2025 exam.
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