The maximum deceleration of a car

[Judas543]

The maximum deceleration of a car...

Homework Statement

The maximum deceleration of a car on a dry road is about 8.0 m/s^2

The Attempt at a Solution

A)
If two cars are moving head-on toward each other at 88 km/h (55 mi/h), and their drivers apply their brakes when they are 85 m apart, will they collide?
Answer: No


B)
How far apart will they be when they stop?
Answer: 10m


C) HELP Drawing the graph and points

On the same graph, plot distance versus time for both cars.
Assume x = 0 is the midpoint between the cars and t = 0 when the brakes are applied. Label the position versus time plot of the car with the positive velocity as x_1(t).
http://img684.imageshack.us/img684/6803/94527989.png

 

[xcvxcvvc]

if x = 0 is the midpoint, car 1 is at x = -85/2 and car 2 is at 85/2 initially.

x(t) = 1/2 a t^2 + v * t + x(i)
so
x_1(t) = 1/2 (-8) * t^2 + 88000/3600 * t - 85/2
x_2(t) = 1/2 8 t^2 - 88000/3600 * t + 85/2
Notice that car 2's velocity is positive (to the right) and its acceleration is negative(to the left). The reverse is true for car 2.

 

[kerimek]

The maximum deceleration of a car on a dry road is about 8.0 m/s^2. This means that the car can slow down at a rate of 8.0 meters per second squared, which is equivalent to 8.0 meters per second per second. This deceleration is dependent on various factors such as the type and condition of the road, the weight and condition of the car, and the driver's reaction time and braking ability.

In order to determine if two cars will collide, we need to calculate the time it takes for each car to come to a complete stop. This can be done by using the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. In this case, both cars have an initial velocity of 88 km/h (55 mi/h) and the same deceleration of 8.0 m/s^2. Therefore, the time it takes for each car to stop is the same, and they will not collide.

To determine the distance between the two cars when they stop, we can use the formula s = ut + 1/2at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity is 88 km/h (55 mi/h), the deceleration is 8.0 m/s^2, and the time is the same for both cars. Plugging these values into the formula, we get a distance of 10 meters between the two cars when they stop.

To plot the distance versus time graph for both cars, we can use the equations s = ut + 1/2at^2 for each car. The graph will have a straight line for the car with the positive velocity (car 1) and a parabola for the car with the negative velocity (car 2). The midpoint between the two cars is labeled as x=0 and the time when the brakes are applied is labeled as t=0. The graph should look similar to the one shown in the question, with the distance for car 1 decreasing linearly and the distance for car 2 decreasing parabolically until they both reach a distance of 10 meters at a certain time.