### Video Transcript

A car of mass 3.6 metric tons was
moving along a straight horizontal road at 18 kilometers per hour when its engine
cut out. Given that it traveled a further
180 meters before it stopped moving, find the magnitude of the resistance to the
movement of the car.

We will begin by sketching a
diagram of the scenario in this question. We are told that the mass of the
car is 3.6 metric tons. Recalling that one ton is equal to
1000 kilograms, we can convert this to kilograms by multiplying by 1000. The mass of the car is therefore
equal to 3600 kilograms. We are told that the carβs engine
cuts out, which means there will be no driving or forward force. And we have been asked to calculate
the magnitude of the resistance to the movement of the car.

Recalling Newtonβs second law πΉ
equals ππ, we know that the sum of our forces is equal to the mass multiplied by
the acceleration. At present, we do not know the
acceleration of the car. However, we can calculate this from
the other information given. We will do this using our equations
of motion or SUVAT equations. The speed of the car when the
engine cut out was 18 kilometers per hour. So we will let the initial velocity
π’ be 18 kilometers per hour. The car traveled a further 180
meters. So this is the displacement π . As the car came to rest, the final
velocity π£ is zero kilometers per hour.

We are trying to calculate the
value of π, the acceleration, in meters per second squared. Before using one of our equations,
we need to convert the velocities from kilometers per hour to meters per second. We know that there are 1000 meters
in one kilometer, and there are 3600 seconds in one hour. We can therefore convert from
kilometers per hour to meters per second by multiplying by 1000 and then dividing by
3600. This is the same as dividing by
3.6.

18 divided by 3.6 is five. And zero divided by 3.6 is
zero. The initial velocity is five meters
per second, and the final velocity, zero meters per second. We will use the equation π£ squared
is equal to π’ squared plus two ππ . Substituting in our values, we have
zero squared is equal to five squared plus two multiplied by π multiplied by
180. This simplifies to zero is equal to
25 plus 360π. We can then subtract 25 from both
sides and divide through by 360 such that π is equal to negative 25 over 360. This simplifies to negative five
over 72.

We now have the acceleration and
mass of the car. Since the friction or resistance
force π
π is acting against the motion, we have negative π
π is equal to 3600
multiplied by negative five over 72. This means that negative π
π is
equal to negative 250, and π
π is equal to 250. The magnitude of the resistance to
the movement of the car is 250 newtons.