Question

A car passes three points A, B and C at \(3\) m/s, \(6\) m/s and \(9\) m/s respectively in a straight line with uniform acceleration. If distance \(AB = 60\) m then find the distance BC.

• A. \(100\) m
• B. \(75\) m
• C. \(200\) m
• D. \(125\) m

Hint:

Use $v^2-u^2=2as$ on each stretch and divide.

Answer 1

The Correct Option is A

Step 1: Find the acceleration from AB
\(v_B^2-v_A^2=2a\cdot AB\) gives \(36-9=2a\times60\), so \(a=\frac{27}{120}=0.225\) m/s\(^2\).

Step 2: Use it on BC
\(v_C^2-v_B^2=2a\cdot BC\) gives \(81-36=2\times0.225\times BC\), so \(45=0.45\,BC\).

Step 3: Solve
\(BC=100\) m. Option (A).

Final Answer:
\(BC=100\) m, option (A). \[ \boxed{\text{(A) }100\text{ m}} \]