Class 12 Applications Of Derivatives · Short Answer2 Marksrelated_rates
Class 12 Maths · Applications Of Derivatives · Short Answer #43
A particle moves on 3y=ax³+1. At x=1 its signed y-rate is twice its nonzero signed x-rate. Find a.
✅ Step-by-Step Solution
Final Answer: a=2
- Differentiate in time: 3ẏ=3ax²ẋ, hence ẏ=ax²ẋ.
- At x=1 use ẏ=2ẋ and ẋ≠0: 2ẋ=a ẋ.
- Therefore a=2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate in time: 3ẏ=3ax²ẋ, hence ẏ=ax²ẋ.
- [1 mark] At x=1 use ẏ=2ẋ and ẋ≠0: 2ẋ=a ẋ.
- [0.5 marks] Therefore a=2.
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