Newton's second law gives the relationship between force applied to an object, its mass and its acceleration:
[tex]F=ma[/tex]
where F is the force, m the mass and a the acceleration.
A force F is applied to football A, whose mass is [tex]m_A[/tex], and so the acceleration of this football will be given by (re-arranging the previous equation)
[tex]a_A = \frac{F}{m_A} [/tex]
Similarly, the acceleration of football B will be
[tex]a_B= \frac{F}{m_B} [/tex]
where [tex]m_B[/tex] is the mass of football B, and where the force F applied to the two footballs is the same.
Since football A has greater mass than football B, [tex]m_A \ \textgreater \ m_B[/tex], if we compare the two previous formula we see that the acceleration of football B is greater than the acceleration of football A:
[tex]a_B \ \textgreater \ a_A[/tex]
Therefore, if the same force is applied to the two footballs, football B will accelerate more than football A.
