I am working on a year 10 physics assignment on road science. I am trying to figure out the reaction distance of a car with:

Skid marks = 24m
Reaction time = 1 sec
Decelaration rate = 6m/sec

I have many formulas in my book and am unsure of which one to use and what the correct answer is. I keep getting different ones. Can you please help?

The reaction distance is how far the car travels before brakes are applied. That equals (reaction time)*(intial velocity)

The initial velocity (V) satisfies the equation
V = sqrt(2 a X),
where a is the deceleration rate and X is the distance travelled while decelerating. Assume that X is the skid mark length (i.e., the wheels lock as soon as the brakes are applied). Thus V = 17 m/s and the reaction distance is 17 m

Thanks for your reponse, it helped greatly. Can you please also tell me if the braking distance is 24metres and it decelerates at rate of 6m/s, does that mean that the time taken to stop after braking would be 4 seconds or do I need to consider anything else to calculate time.

The braking distance (not counting the time travelled during the reaction time) is 24 m.

Since V = 17 m/s and the average V is V/2 = 8.5 m/s while brakes are applied, the time spent decelerating is
24 m/(8.5 m/s) = 2.82 s

No, you cannot say that X/V = stopping time.

Add 1.0 s (the reaction time) to 2.82 s and you get a total time to stop of 3.82 s. This would be measured from the instant the driver decides to brake, but has not begun decelerating.

Thanks again for the help, I am now getting there with my assignment. Just one more question though. If I doubled the weight of the car, would the deceleration rate change from 6m/s to 12m/s?

Of course! I would be happy to help you with your physics assignment on road science. To calculate the reaction distance of a car, we need to consider three factors: the skid marks, the reaction time, and the deceleration rate.

The reaction distance is the distance traveled by a car during the driver's reaction time. It can be calculated using the formula:

Reaction Distance = Reaction Time × Initial Velocity

To calculate the initial velocity, we need to use the following formula:

Initial Velocity = Final Velocity - (Deceleration Rate × Stopping Time)

The stopping time can be determined from the skid marks and the deceleration rate using the formula:

Stopping Time = Skid Marks / Deceleration Rate

Now, let's plug in the given values:

Skid Marks = 24m
Reaction Time = 1sec
Deceleration Rate = 6m/sec

First, we'll find the stopping time:

Stopping Time = Skid Marks / Deceleration Rate
Stopping Time = 24m / 6m/sec
Stopping Time = 4sec

Next, let's calculate the initial velocity:

Initial Velocity = Final Velocity - (Deceleration Rate × Stopping Time)
Since the car came to a stop, the Final Velocity is 0.

Initial Velocity = 0 - (6m/sec × 4sec)
Initial Velocity = -24m/sec

Now, we can find the reaction distance:

Reaction Distance = Reaction Time × Initial Velocity
Reaction Distance = 1sec × -24m/sec
Reaction Distance = -24m

The negative sign indicates that the car traveled backward during the reaction time, which is not physically possible. Therefore, the reaction distance in this case is 0 meters.

To summarize, the reaction distance of the car in this scenario is 0 meters.