Question

at a place where the acceleration due to gravity is 10 M per second square a force of 5 kg weight act on a body of mass 10 kg initially at rest the velocity of the body after 4 seconds

Answer 1

When Isaac Newton wrote F=ma, the concepts of force, mass and acceleration were new to people. In fact, the expression is sometimes described as “defining mass.” In any case, the numbers are pretty simple here to figure out the acceleration, which appears to be constant.

A constant acceleration means that the velocity v = at grows as a straight line. It starts at zero and then climbs linearly to 5a at 5 seconds

You can figure the total displacement in this 5 seconds as the average velocity times time. That is, the average velocity is 1/2*5a (since it started at zero and climbed to 5a linearly). Just multiple that by time 5. Or you can see that the formula given in Joshua’s answer works, which is 1/2at^2, for this period.

Then for the next 5 seconds, the velocity, which is 5a, is constant. Then the additional distance is just 5a*5 seconds. Add the two together for the final result.

(One final comment - units help. Since the units of acceleration will be m/s^s, to get to a velocity in m/s you have to multiply by a time in seconds. Then to get to a length in meters, you have to multiply again by a time in seconds.)