The minimum distance required to stop a car

[evomunkie]

The minimum distance required to stop a car moving at 44.0 mi/h is 42.0 ft. What is the minimum stopping distance for the same car moving at 77.0 mi/h, assuming the same rate of acceleration?

how do i go about doing this problem.? pls help.

 

[cristo]

Well, you need to find out the acceleration of the first car. Do you know a formula that relates acceleration to velocity and time?

 

[m2003]

I would approach this problem by using the principles of physics and the laws of motion. The minimum distance required to stop a car depends on several factors, including the initial speed of the car, the rate of acceleration, and the coefficient of friction between the tires and the road surface.

To calculate the minimum stopping distance for a car moving at 77.0 mi/h, we can use the equation:

d = (v^2)/(2a)

Where d is the stopping distance, v is the initial velocity, and a is the acceleration.

In this case, we know that the initial velocity (v) is 77.0 mi/h, and the stopping distance (d) is unknown. We also know that the rate of acceleration (a) will be the same as the previous scenario, as it is determined by the braking system of the car.

Substituting these values into the equation, we get:

d = (77.0 mi/h)^2 / (2a)

To solve for d, we need to first convert the initial velocity from miles per hour to feet per second, as the units need to be consistent. We can do this by multiplying 77.0 mi/h by 1.47 ft/s (1 mi/h = 1.47 ft/s). This gives us an initial velocity of 113.19 ft/s.

Substituting this value into the equation, we get:

d = (113.19 ft/s)^2 / (2a)

We can now calculate the minimum stopping distance by plugging in the known value for a, which is 42.0 ft (from the previous scenario):

d = (113.19 ft/s)^2 / (2 * 42.0 ft)

Solving this equation gives us a minimum stopping distance of 163.38 ft.

Therefore, the minimum stopping distance for the same car moving at 77.0 mi/h is 163.38 ft, assuming the same rate of acceleration and coefficient of friction. This is significantly longer than the minimum stopping distance of 42.0 ft at 44.0 mi/h, highlighting the importance of adjusting our driving behavior and maintaining a safe following distance when traveling at higher speeds.