Tom and Jerry relive!

I think the question means at what value of B will jerry just escape. This can be solved with the help of relative motion. Just assume Jerry is stationary and just give his acceleration to Tom in the opposite direction. We would have 2 equations, (B - A)t = u ; d = ut + 0.5(B - A)t^2. Solving these would give you the value of B as 5

Let us utilize the equation $x = v_{0}t + \frac{1}{2}at^2$ from uniform acceleration kinematics. If Jerry runs a distance $x$ in $t$ seconds, then Tom runs a distance $d+x$ to catch him in $t$ seconds. This can be modeled via:

Tom: $d+x = ut + \frac{1}{2}\alpha t^2$ (i)

Jerry: $x = \frac{1}{2}\beta t^2$ (ii)

If we substitute (ii) into (i), we end up with a quadratic equation in $t$ :

$d + \frac{1}{2}\beta t^2 = ut + \frac{1}{2}\alpha t^2$ ;

or $\frac{1}{2}(\beta - \alpha) t^2 - ut + d = 0;$

or $\large t = \frac{u \pm \sqrt{u^2 - 4(d)((\beta-\alpha)/2)}}{\beta-\alpha}$ (iii).

Tom will just capture Jerry when the discriminant in (iii) equals zero, or:

$\sqrt{u^2 - 4(d)((\beta-\alpha)/2)} = 0$ ;

or $\sqrt{5^2 - 4(5)(\beta - 2.5)(1/2)} = 0;$

or $\sqrt{50-10\beta} = 0;$

or $\boxed{\beta = 5 m/s^{2} }$ .