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(B) The initial velocity $u = 10 \,m/s$ and acceleration $a = 2 \,m/s^2$.Using the equation of motion $S = ut + \frac{1}{2}at^2$ for a time interval $

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$\frac{19}{17}$

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(B) The initial velocity $u = 10 \,m/s$ and acceleration $a = 2 \,m/s^2$.Using the equation of motion $S = ut + \frac{1}{2}at^2$ for a time interval $\Delta t = 1 \,s$:For $S_1$ (interval $t=3 \,s$ to $t=4 \,s$):The velocity at $t=3 \,s$ is $v_3 = u + at = 10 + 2(3) = 16 \,m/s$.$S_1 = v_3(1) + \frac{1}{2}a(1)^2 = 16(1) + \frac{1}{2}(2)(1)^2 = 16 + 1 = 17 \,m$.For $S_2$ (interval $t=4 \,s$ to $t=5 \,s$):The velocity at $t=4 \,s$ is $v_4 = u + at = 10 + 2(4) = 18 \,m/s$.$S_2 = v_4(1) + \frac{1}{2}a(1)^2 = 18(1) + \frac{1}{2}(2)(1)^2 = 18 + 1 = 19 \,m$.Therefore, the ratio $\frac{S_2}{S_1} = \frac{19}{17}$.

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