A small car with a weight of 2000 lb traveling at 30 mph can stop in about 100 ft. How far does it take for a large SUV weighing 8000 lb to stop if it is also traveling at 30 mph?

100 ft

To determine how far it would take for the large SUV to stop, we can use the concept of kinetic energy and braking distance. The kinetic energy of a moving object is given by the formula:

KE = 0.5 * mass * velocity^2

where KE is the kinetic energy, mass is the mass of the object, and velocity is the speed of the object.

Since both the small car and the SUV are traveling at the same speed, their kinetic energies will be equal. We can set up the following equation:

0.5 * mass_car * velocity^2 = 0.5 * mass_SUV * velocity^2

Canceling out the terms that are the same on both sides of the equation, we get:

mass_car = mass_SUV

Given that the weight of the small car is 2000 lb, we can convert it to mass by dividing by the acceleration due to gravity (32.2 ft/s^2):

mass_car = 2000 lb / 32.2 ft/s^2

mass_car = 62.11 slugs

Now we can solve for the stopping distance of the SUV using the formula for kinetic energy:

KE = 0.5 * mass * velocity^2

Rearranging the formula to solve for the stopping distance:

stopping distance = KE / (0.5 * mass)

Plugging in the values for the SUV:

stopping distance_SUV = KE / (0.5 * mass_SUV)

stopping distance_SUV = KE / (0.5 * 8000 lb / 32.2 ft/s^2)

stopping distance_SUV = KE / (400 lb / ft/s^2)

Next, we need to find the kinetic energy of the small car. We can use the formula:

KE = 0.5 * mass * velocity^2

Plugging in the values for the small car:

KE = 0.5 * mass_car * velocity^2

KE = 0.5 * 62.11 slugs * (30 mph)^2

Finally, substituting the values into the equation for stopping distance of the SUV:

stopping distance_SUV = (0.5 * 62.11 slugs * (30 mph)^2) / (400 lb / ft/s^2)

stopping distance_SUV = 62.11 slugs * (30 mph)^2 / 400 lb / ft/s^2

Calculating the stopping distance:

stopping distance_SUV = 69.15 ft

Therefore, it would take the large SUV, weighing 8000 lb, about 69.15 ft to stop if it is traveling at 30 mph.