Displacement $x$ versus $t^2$ graph is shown for a particle. The acceleration of the particle is

• Correct answer
  A

  $4 \mathrm{m} {\mathrm{s}}^{-2}$
• B

  $8 \mathrm{m} {\mathrm{s}}^{-2}$
• C

  Zero
• D

  $2 \mathrm{m} {\mathrm{s}}^{-2}$

Solution

From the graph,

$x=\mathrm{S}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}\left(t^2\right)$

$x=\frac{2-0}{1-0}\left(t^2\right)$

$x=2t^2$

$\frac{dx}{dt}=4\mathrm{t}$

$\frac{d^{2}x}{d{t}^2}=4$

$a=4\mathrm{ m} {\mathrm{s}}^{-2}$ $\left[\because \frac{d^{2}x}{d{t}^2}=a\right]$

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