Abus driver makes an emergency stop by slamming on the bus's brakes. later, he slams on the brakes
again with the same amount of force but this time his speed is twice as much as the first time. how far will
the bus skid compared to the first time?
a. the stopping distance stays the same.
b. the stopping distance is doubled.
c. the stopping distance is quadrupled.
d. the stopping distance is tripled.
e. the mass of the bus is required.

Option C

Explanation: Let's do a heavy simplification.

The kinetic energy of the bus is K = (m/2)*v^2

Where m is the mass of the bus, and v is the velocity of the bus.

When the brakes are used, we can do a linear relationship that gives us the distance that the bus needs to come to a full stop, and this will depend on the kinetical energy that the buss had just right before, so the distance that the bus moves after slamming on the brakes is:

D = K/F = ((m/2)*v^2)/F

Where F depends on the effectiveness of the brakes, as bigger F is, faster the bus comes to a full stop.

Now, if we double the velocity; we have:

D' = ((m/2)*(2*v)^2)/F = ((m/2)*4*v^2)/F = 4*(((m/2)*v^2)/F) = 4*D

D' = 4D

So the distance is quadrupled, then the correct option is C

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.