Answer:
The distance each vehicle travels before coming to a stop depends on its initial speed, mass, and the coefficient of friction between its tires and the road surface. However, since the car and truck have the same coefficients of static and kinetic friction between their tires and the road surface, their stopping distances will be directly proportional to their masses.
To calculate the stopping distances, we can use the following formula for the distance traveled during a constant deceleration:
d = v^2 / 2a
where d is the stopping distance, v is the initial velocity, and a is the deceleration. The deceleration is related to the coefficient of friction and the gravitational acceleration as follows:
a = μg
where μ is the coefficient of friction and g is the gravitational acceleration (9.81 m/s^2).
For the car, the initial velocity is not given, so let's assume it was traveling at 30 m/s (108 km/h) before the brakes were applied. Then, the deceleration is:
a = μg = μ × 9.81 m/s^2
For the car, the mass is 2000 kg, so the stopping distance is:
d_car = v^2 / 2a = 900 / (2 × μ × 9.81) = 45.84 / μ
For the truck, we can use the same formula, but with the mass of 7500 kg:
d_truck = v^2 / 2a = 900 / (2 × μ × 9.81 × 7500/2000) = 153.12 / μ
Therefore, the truck travels a greater distance before stopping than the car, by a factor of 153.12 / 45.84 = 3.34, assuming they were traveling at the same initial speed.