Question

Tom and his little sister are enjoying an afternoon at the ice rink. they playfully place their hands together and push against each other. tom's mass is 61 kg and his little sister's mass is 15 kg. if the sister's acceleration is 2.1 m/s2 in magnitude, what is the magnitude of tom's acceleration?

Answer 1

Newton's third law says:
"For every action, there is an equal and opposite reaction. ".

So, the force that Tom does on the sister is equal to force the sister applies on Tom:
$F_t = F_s$
where the label "t" means "on Tom", while the label "s" means "on the sister".

From Newton's second law, we also know
$F=ma$
where m is the mass and a the acceleration. so we can rewrite the first equation as
$m_t a_t = m_s a_s$
And find Tom's acceleration:
$a_t = \frac{m_s}{m_t} a_s = \frac{15 kg}{61 kg} (2.1 m/s^2) =0.52 m/s^2$