Question:
A body moving with uniform acceleration travel \(16\) m in the third second of its motion and \(24\) m in the fifth second of its motion. The velocity of the body in \(10\) second is
A body moving with uniform acceleration travel \(16\) m in the third second of its motion and \(24\) m in the fifth second of its motion. The velocity of the body in \(10\) second is
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Use the formula for distance covered in the nth second to get u and a.
Updated On: Nov 12, 2026
- \(42\) m/s
- \(46\) m/s
- \(50\) m/s
- \(56\) m/s
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Distance in the nth second is \(S_n=u+\dfrac{a}{2}(2n-1)\).
Step 2: Calculation
\(S_3=u+2.5a=16\) and \(S_5=u+4.5a=24\).
Subtracting gives \(2a=8\), so \(a=4\) m/s\(^{2}\) and \(u=6\) m/s.
Step 3: Velocity after 10 s
\(v=u+at=6+4\times10=46\) m/s.
Final Answer:
The velocity of the body after 10 seconds is 46 m/s. \[ \boxed{\text{(B) }46\ \text{m/s}} \]
Distance in the nth second is \(S_n=u+\dfrac{a}{2}(2n-1)\).
Step 2: Calculation
\(S_3=u+2.5a=16\) and \(S_5=u+4.5a=24\).
Subtracting gives \(2a=8\), so \(a=4\) m/s\(^{2}\) and \(u=6\) m/s.
Step 3: Velocity after 10 s
\(v=u+at=6+4\times10=46\) m/s.
Final Answer:
The velocity of the body after 10 seconds is 46 m/s. \[ \boxed{\text{(B) }46\ \text{m/s}} \]
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