A car crashes into a concrete wall

[envscigrl]

Here it is:
A 2000-kg car traveling at 85.0 km/h crashes into a concrete wall that does not give at all. Estimate the time of the collision, assuming that the center of the car travels halfway to the wall with constant deceleration. (Use 5.75 m for the length of the car.)

I know I need to use the equations of kinematic motion to find acceleration and then find time from that. But I am so confused as to what I use for delta x in the equations. I know it somehow involves the center of mass of the car but I don't know how. I have tried solving with just the lenghth of the car as it is given (5.75) and have also tried dividing it by two and four but neither worked. How do I solve this?

 

[Tide]

If the decleration is constant then the starting speed is related to the distance required to stop by

$$v = \sqrt {2 a d}$$

from which you can work out the acceleration since you know the initial speed and the distance.

 

[wais]

To solve this problem, we first need to calculate the initial velocity of the car before the crash. We can use the given speed of 85.0 km/h and convert it to m/s by multiplying it by 1000/3600, which gives us an initial velocity of 23.6 m/s.

Next, we need to find the final velocity of the car at the moment of impact. Since the car crashes into a concrete wall that does not give at all, the final velocity will be 0 m/s.

Now, we can use the equation v^2 = u^2 + 2as to find the deceleration (a) of the car. We know that the initial velocity (u) is 23.6 m/s, the final velocity (v) is 0 m/s, and the distance traveled (s) is half the length of the car, which is 5.75/2 = 2.875 m. Plugging in these values, we get a = -17.1 m/s^2.

Finally, we can use the equation v = u + at to find the time (t) of the collision. Again, we know the initial velocity (u) and deceleration (a), so we can plug those in and solve for time. We get t = 23.6/17.1 = 1.38 seconds.

Therefore, the estimated time of the collision is 1.38 seconds. Keep in mind that this is an approximation and the actual time may vary slightly due to factors such as air resistance and friction.