CUET · MATHS · PYQ PAPER 2023
A car starts from a point at time \(t = 0\) seconds and stops at Q.
The distance \(x\) in meters covered by it in \(t\) seconds is given by
\(x = t^2 \left( 2 - \frac{t}{3} \right)\).
The time taken by it to reach Q is:
- A 4 seconds
- B 0 seconds
- C \(\frac{1}{3}\) seconds
- D 2 seconds
Answer & Solution
Correct Answer
(A) 4 seconds
Step-by-step Solution
Detailed explanation
\(v = \frac{dx}{dt} = \frac{d}{dt} \left( 2t^2 - \frac{t^3}{3} \right) = 4t - t^2\) At stop, \(v = 0\) \(4t - t^2 = 0\) \(t(4 - t) = 0\) \(t = 4\) seconds (as \(t=0\) is the start time)
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