Does the mass of the car matter when driving on the road? When skidding?

Answer 1

Friction is dependent on the mass of the car, yes, weight requires more engine power/fuel to keep it going against road friction.

When skidding? You want a lot of friction to stop, however, increasing mass also increases momentum. Consider this, skidding to stop a car:
forcefriction*distance=mass*velocity
mu*mass*g*distance=mass*Velocity
distance=velocity/(mu*g)

so braking distance depends on initial velocity, coefficent of friction...not mass.

Answer 2

oops, error.
forcefriction*distance=1/2 *mass*velocity^2
mu*mass*g*distance=1/2 *mass*Velocity^2
distance=velocity^2/(2mu*g)
so braking distance depends on initial velocity squared, and the coefficent of friction...not mass.

Answer 3

Thank You!