# 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 \(12\; m/ s^{-1} ?\)

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.

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 \((N).\)