# Question #7f631

##### 1 Answer

#### Answer:

#### Explanation:

Start by converting the speed of the car from *kilometers per hour* to *meters per second*

#85 color(red)(cancel(color(black)("km")))/color(red)(cancel(color(black)("h"))) * (10^3"m")/(1color(red)(cancel(color(black)("km")))) * (1color(red)(cancel(color(black)("h"))))/"3600 s" = "23.61 m s"^(-1)#

Now, notice that the car goes from a speed of **negative**.

In other words, the car is **decelerating**, which means that its *acceleration* is acting in the opposite direction to its direction of movement.

Another thing to notice here is that the speed of the car is decreasing **significantly** over a very short distance. From the moment of impact, it takes only

#d = "0.85 m"#

for the speed of the car to decrease by **very high absolute value**, i.e. its magnitude will be very high.

Your tool of choice here will be this equation

#color(blue)(ul(color(black)(v_f^2 = v_0^2 + 2 * a * d)))#

Here

#v_f# is thefinal speedof the car#v_0# is itsinitial speed, i.e. its speed before the impact#a# is its acceleration#d# is the distance covered by the driver after the impact

Rearrange the above equation to solve for

#2 * a * d = v_f^2 - v_0^2 implies a = (v_f^2 - v_0^2)/(2 * d)#

Plug in your values to find

#a = ( 0^2 "m"^color(red)(cancel(color(black)(2))) "s"^(-2) - 23.61^2 "m"^color(red)(cancel(color(black)(2))) "s"^(-2))/(2 * 0.85 color(red)(cancel(color(black)("m")))) = -"327.9 m s"^(-2)#

As you can see, the acceleration is indeed *negative*. Convert the acceleration to

#-327.9 color(red)(cancel(color(black)("m s"^(-2)))) * "1.00g"/(9.80color(red)(cancel(color(black)("m s"^(-2))))) = color(darkgreen)(ul(color(black)(-"33.4g")))#

I'll leave the answer rounded to three **sig figs**.