Example Problem with Complete Solution

1B-2 : Mass, Force and Acceleration 4 pts
A strong boy throws a rock straight up with a force of 100 N. At what rate does the rock initially accelerate upwards, in m/s2? Assume the mass of the rock is 2 kg and the local gravitational acceleration is 9.74 m/s2.
Read: The key here is to recognize that two forces are acting on the rock: the 100 N and the weight of the rock (due to gravity).  Then, the problem becomes an application of Newton's 1st Law of Motion.
Given: m 2 kg g 9.74 m/s2
Fthrow 100 N
Find: a ??? m/s2
Assumptions: None.
Equations / Data / Solve:
The key equation here is Newton's 1st Law of Motion :
Eqn 1
We can solve Eqn 1 for the rate at which the rock accelerates :
Eqn 2
We know that : gC 1 kg-m/N-s2
So, all we need to is determine the net force acting on the stone.
A free-body diagram might be helpful.
The net force acting on the rock in the upward direction is :
Eqn 3
We can apply Newton's 1st Law of
 Motion again to evaluate Fwt.
Eqn 4
We can solve Eqn 4 for Fwt, as follows :
Eqn 5
Plugging values into Eqn 5, then Eqn 3 and, finally, Eqn 2 yields : Fwt 19.5 N
Fnet 80.52 N
a 40.26 m/s2
Answers: a 40.3 m/s2