Question:
The distance travelled by a moving particle is given by $s=t^{2}-6t+10$. The particle is at rest when $t=$ ________.
The distance travelled by a moving particle is given by $s=t^{2}-6t+10$. The particle is at rest when $t=$ ________.
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Velocity is the first derivative of displacement.
Updated On: Jun 26, 2026
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The Correct Option is D
Solution and Explanation
Step 1: Concept
A particle is "at rest" when its velocity $v = \frac{ds}{dt} = 0$.
Step 2: Meaning
Differentiate $s = t^2 - 6t + 10$ with respect to $t$.
Step 3: Analysis
$v = 2t - 6$. Set $2t - 6 = 0 \implies 2t = 6 \implies t = 3$.
Step 4: Conclusion
The particle is at rest at $t = 3$ seconds. Final Answer: (D)
A particle is "at rest" when its velocity $v = \frac{ds}{dt} = 0$.
Step 2: Meaning
Differentiate $s = t^2 - 6t + 10$ with respect to $t$.
Step 3: Analysis
$v = 2t - 6$. Set $2t - 6 = 0 \implies 2t = 6 \implies t = 3$.
Step 4: Conclusion
The particle is at rest at $t = 3$ seconds. Final Answer: (D)
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