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(D) Let the two particles be $A$ and $B$. The initial separation between them is $x_0 = 100 \ m$.Both particles start from rest,so their initial veloc

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zero

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(D) Let the two particles be $A$ and $B$. The initial separation between them is $x_0 = 100 \ m$.Both particles start from rest,so their initial velocities are $u_A = 0$ and $u_B = 0$.Both particles have the same acceleration $a_A = a_B = 10 \ m/s^2$.The displacement of particle $A$ after time $t = 10 \ s$ is $s_A = u_A t + \frac{1}{2} a_A t^2 = 0 + \frac{1}{2} (10)(10)^2 = 500 \ m$.The displacement of particle $B$ after time $t = 10 \ s$ is $s_B = u_B t + \frac{1}{2} a_B t^2 = 0 + \frac{1}{2} (10)(10)^2 = 500 \ m$.The relative displacement is given by $\Delta s = s_A - s_B = 500 - 500 = 0 \ m$.Alternatively,the relative acceleration $a_{rel} = a_A - a_B = 10 - 10 = 0 \ m/s^2$ and relative initial velocity $u_{rel} = u_A - u_B = 0 \ m/s$. Thus,the relative displacement $s_{rel} = u_{rel} t + \frac{1}{2} a_{rel} t^2 = 0$.

Two particles are at rest on a straight track and they are separated from each other by $100 \ m$. They start their motion in the same direction,with the same acceleration $10 \ m/s^2$. Their relative displacement after $10 \ s$ will be

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