Check your intuition with this simple problem...!

Classical Mechanics Level 2

A truck and a car move on a road both with velocity V V . The asphalt is uniform and the tires of both the car and the truck are made of exacly the same material.

Suddenly the drivers see a deer in the middle of the road and slam the brakes simultaneously.

Both vehicles start to slide. Choose the correct statement.

Not enough information. The truck will stop first. Both the car and the truck will stop at the same time. The car will stop first.

Konstantinos Manos by Konstantinos Manos , 23, Greece

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1 solution

After slamming the brakes the truck and the car experiecne a kinetic friction force.

Knowing that the asphalt is uniform and the tire material identical, we can safely assume that the coefficient of kinetic friction μ \mu is the same in both cases.

Σ F c a r = m ⋅ a c a r = m ⋅ g ⋅ μ ΣF_{car} = m \cdot a_{car} = m \cdot g \cdot \mu

which means:

a c a r = g ⋅ μ \boxed{a _{car} = g \cdot \mu }

Σ F t r u c k = M ⋅ a t r u c k = M ⋅ g ⋅ μ ΣF_{truck} = M \cdot a_{truck} = M \cdot g \cdot \mu

a t r u c k = g ⋅ μ \boxed{a _{truck} = g \cdot \mu}

Both decelerations and initial velocities are the same, so the required time interval for the truck and the car to stop are the same. The masses play NO role!

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