Q77 / 90 · JEE Main 2024 (04 Apr Shift 1) · Physics

A body travels $102.5 \mathrm{~m}$ in $\mathrm{n}^{\text {th }}$ second and $115.0 \mathrm{~m}$ in $(\mathrm{n}+2)^{\text {th }}$ second. The acceleration is :

  • Correct answer
    A
    $6.25 \mathrm{~m} / \mathrm{s}^2$
  • B
    $12.5 \mathrm{~m} / \mathrm{s}^2$
  • C
    $9 \mathrm{~m} / \mathrm{s}^2$
  • D
    $5 \mathrm{~m} / \mathrm{s}^2$

Solution

$\begin{aligned} & \text { Given, } 102.5=\mathrm{u}+\frac{\mathrm{a}}{2}(2 \mathrm{n}-1) \& \\ & 115=\mathrm{u}+\frac{\mathrm{a}}{2}(2 \mathrm{n}+3) \\ & \Rightarrow 102.5=\mathrm{u}+\mathrm{an}-\frac{\mathrm{a}}{2} \& \\ & 115=\mathrm{u}+\mathrm{an}+\frac{3 \mathrm{a}}{2} \\ & 12.5=2 \mathrm{a} \Rightarrow \mathrm{a}=6.25 \mathrm{~m} / \mathrm{s}^2 \end{aligned}$

Hence, the correct answer is option: 'A'.

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