Question

Jeremy accidently dropped his toy stuffed animal from the balcony of his apartment on the fourth floor. The toy hit the ground at a velocity of 16.0 meters/second. At impact, it took 2.0 seconds for the toy’s velocity to reach 0 meters/second. If the toy has a mass of 0.25 kilograms, what's the force of the impact?

Answer 1

According to the second law of motion, force is the product of mass times acceleration. If we were to solve for the force, we would need the acceleration and the mass. 

Acceleration was not given in the problem, but we can solve for it by using the velocity and the time because by definition, acceleration is the change in velocity over time. 

$a = \frac{vf-vi}{t}$

The initial velocity is 16.0m/s because it is the first recorded time. The final is 0 m/s or the last recorded velocity. The time we will use is 2.0 s because it is the time the change in velocity occurred. 

$a = \frac{vf-vi}{t}$
$a = \frac{0m/s-16.0m/s}{2.0s}$
$a = \frac{-16.0m/s}{2.0s}$
$a=-8.0m/ s^{2}$

Now that we have acceleration, we can now solve for the Force. Again Force is the product of mass and acceleration. 

$F=ma$
$F=(0.25kg)(-8.0m/ s^{2} )$
$F=-2kg.m/ s^{2} )$ or $-2N$

The force is -2N. Now if you are looking for the magnitude of the force then you can just put 2N.

The negative sign indicates the direction of the force, if it is negative this means that the force applied was in the opposite direction.