### Video Transcript

A body of mass 96 kilograms was
moving in a straight line at 17 meters per second. A force started acting on it in the
opposite direction to its motion. As a result, over the next 96
meters, its speed decreased to 11 meters per second. Using the work–energy principle,
determine the magnitude of the force.

In the problem, we are instructed
to use the work–energy principle. In equation form, this states that
the net work down on an object is equal to the change in kinetic energy of the
object. Recalling that work is defined as
force times displacement, where the force is parallel to the displacement, we can
expand out our formula, replacing 𝑊 with 𝐹 times 𝑑. Change in kinetic energy is the
final kinetic energy minus the initial kinetic energy. We should remember that the kinetic
energy of an object is equal to one-half 𝑚𝑣 squared, where 𝑚 is the mass of the
object and 𝑣 is the speed of the object. We can replace kinetic energy final
with one-half 𝑚𝑣 final squared and kinetic energy initial with one-half 𝑚𝑣
initial squared. To isolate the force, we can divide
both sides of the equation by 𝑑, which will cancel out the displacement on the left
side.

Now that we have an expression for
our force, we can substitute in the values from our problem. We use 96 for the mass, 11 for the
final velocity, 17 for the initial velocity, and 96 for the displacement. When we multiply out our first
term, one-half times 96 times 11 squared, we get 5,808. Multiplying out the second term of
one-half times 96 times 17 squared, we get 13,872. When we subtract our numerator and
divide by our denominator, we get a force of negative 84 newtons. We are asked to find the magnitude
of the force, and therefore we do not need the negative sign as that tells us the
direction. Using the work–energy principle,
the magnitude of the force acting on the object is 84 newtons.