Accelaration/ traveling problem

[Teenytiny1991]

Homework Statement

A camero runs a red light and hits an suv directly behind where a tv news crew is filming. from the sound of the dqueling tires recorded on film, the police can tell that the driver applied his breaks for exactly 1.69 secs. a csi team review the clip and determines the care decelerated at a constant rate of -10.2 m/s^2 prior to the impact. the skid marks determined he breaked for 48.2 meters
A) how fast was the camero going before the driver applied the breaks
B) how fast was the camero traveling when it hit the suv

Homework Equations

The Attempt at a Solution

-10.2 m/s^2 x 1.69 sec/ 48.2 m i don't think i set it up crrectly =(

 

[tiny-tim]

Hi Teenytiny1991!

(try using the X² tag just above the Reply box )

You have a s and t, and you want u and v.

Which of the standard constant acceleration equations should you use?

What do you get? ​

 

[kerimek]

As a scientist, it is important to approach this problem with a systematic and mathematical approach. Let's start by identifying the given information:

- The driver applied the brakes for 1.69 seconds.
- The car decelerated at a constant rate of -10.2 m/s^2.
- The skid marks measured 48.2 meters.

To solve this problem, we can use the equation:

vf = vi + at

Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time

A) To determine the initial velocity of the camero, we can rearrange the equation to solve for vi:

vi = vf - at

Substituting the given values, we get:

vi = 0 m/s - (-10.2 m/s^2 x 1.69 sec)

vi = 17.238 m/s

Therefore, the camero was traveling at 17.238 m/s or approximately 61.66 km/h before the driver applied the brakes.

B) To determine the velocity of the camero when it hit the suv, we can use the equation:

vf^2 = vi^2 + 2ad

Where:
vf = final velocity
vi = initial velocity
a = acceleration
d = distance

Substituting the given values, we get:

vf^2 = (17.238 m/s)^2 + 2(-10.2 m/s^2)(48.2 m)

vf^2 = 296.966 m^2/s^2

vf = √296.966 m^2/s^2

vf = 17.238 m/s

Therefore, the camero was traveling at 17.238 m/s or approximately 61.66 km/h when it hit the suv.

In conclusion, the camero was traveling at a speed of 61.66 km/h before the driver applied the brakes and maintained the same speed when it hit the suv. It is important to note that this is a simplified calculation and does not take into account other factors such as friction and air resistance.