# Biophysics Problem 8

What horizontal force will stop, in  $4 \; \text{seconds,}$ a $5\; kg$  mass sliding on a frictionless floor if the mass has an initial speed of  $12\; m/ s^{-1} ?$

#### First Step

If you knew the acceleration then this should be a simple exercise of applying Newton's second law  $(F=ma).$

To find the acceleration you will have to use one of the kinematic equations, each of which uses 4 of the variables. (ie: initial velocity, final velocity, distance, time, and acceleration).

List the three variables given and the one you wish to find.

#### Caculations

Your list of known values should be:

$\text{initial velocity} \; u = 15 \;m/s \\ \text{final velocity} \; v = 0 \;m/s \\ \text{time} \; t = 4\;s$

You wish to find acceleration '$a$'.

Write down the equation you would use to solve for '$a$'.

You should be using the formula

$v = u + at$

Now solve for the acceleration $a$.

Substitution into  $v = u + at \;a$ should give:

$v = u + at \\ 0 = 15 \;m/s + a \times 4 \;s$

solve this to get:

$a = -3 \;m/s^2$

So the magnitude of the acceleration is $3.$

Substitute into Newton's second law to find the force required to stop the mass.

The correct answer is $15 \;N.$

Remember to specify the magnitude $(15)$ as well as the units $(N).$