Hi,
Really having problems with this question. Anyone can help me please?
Thanks

Well, first, the picture doesn't seem to belong to the question since the question mentions a horizontal table...

To find the acceleration of the system, you need to consider the two bodies separately at first.

On the 10 kg mass, you have tension and friction acting on it. Assuming that the particle pulls the mass, we have:

T - Ff = ma

T is the tension, Ff is the frictional force, m is the mass of the 10 kg mass and a is the acceleration of the mass.

On the particle, we have:

mg - T = ma

mg is the weight of the particle, T is the tension, m is the mass of the particle and a is the acceleration of the particle.

Substitute the values that you are given and solve simultaneously the two equations to get T and a.

a goes in part (a),
T goes in part (b),
When you get a, you can find part (c) using kinematics.