Calculate the total stopping distance of the car

In summary, the reaction time of a driver to brake is 0.5 seconds, during which the speed remains constant. The speed of the car is initially 50 km/h and it decelerates at a rate of 6.0 m/s^2 to come to a stop. The total stopping distance of the car can be calculated using the equation d = vt + 1/2at^2, where v is the initial speed, a is the acceleration, and t is the time. The driver travels 6.945 m during the reaction time period of 0.5 seconds, and the total stopping distance is 23.03 m.
  • #1
eefje
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Homework Statement


reaction time of a driver to brake is 0,5s in that time the speed is constant
the speed of a car is constant when he decides to slow down and to stop with -6,0 m/s2, the initial speed is 50 km/h
Calculate the total stopping distance of the car

Homework Equations


Ve= -6,0*t +13,89
t=2,3
xe=-6,0*(2,3)^2 +13,89*2,3
what did I do wrong?

The Attempt at a Solution


the solution has to be 23,03 m but I can't solve it,
 
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  • #2
Hi eefje, Welcome to Physics Forums.

FYI, you should list the standard equations that you will use in the relevant equations section, then show how you applied them in your attempt at a solution.

I see that you didn't account for the distance traveled during the driver's reaction time period. How far does he travel before he bgins to decelerate?
 
  • #3
gneill said:
Hi eefje, Welcome to Physics Forums.

FYI, you should list the standard equations that you will use in the relevant equations section, then show how you applied them in your attempt at a solution.

I see that you didn't account for the distance traveled during the driver's reaction time period. How far does he travel before he bgins to decelerate?
Hey Thank you for helping me, I will do it right the next time.
In the 0,5 s he travels 6,945m i think (13,89*0,5). But I still can't solve it
 
  • #4
What basic equation are you applying for the period in which he decelerates?
 
  • #5
gneill said:
What basic equation are you applying for the period in which he decelerates?
you mean in the 0,5s ? Δv= Δx/ Δt

and after that: Δx= a*Δt^2+Δv*t
Δv=a*Δt
 
  • #6
eefje said:
you mean in the 0,5s ? Δv= Δx/ Δt

and after that: Δx= a*Δt^2+Δv*t
Δv=a*Δt
You're good for the first period (reaction time period). ##d = vt##

For the second period where acceleration is happening you want the standard kinematic formula ##d = v_o t + \frac{1}{2} a t^2##.
Note the "1/2" constant that multiplies the acceleration term.
 
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  • #7
gneill said:
You're good for the first period (reaction time period). ##d = vt##

For the second period where acceleration is happening you want the standard kinematic formula ##d = v_o t + \frac{1}{2} a t^2##.
Note the "1/2" constant that multiplies the acceleration term.
Thank you very much, I can solve it now. the 1/2 was a stupid mistake, but I didn't know that the distance in the 0,5 s important was. Thank you :)
 
  • #8
You're welcome. Good luck in your studies.
 
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1. What factors affect the total stopping distance of a car?

The total stopping distance of a car is affected by several factors, including the speed of the car, the condition of the brakes, the condition of the tires, and the road surface. Other factors such as weather conditions and the weight of the car can also play a role in the stopping distance.

2. How is the total stopping distance of a car calculated?

The total stopping distance of a car is calculated by adding together the thinking distance and the braking distance. The thinking distance is the distance the car travels while the driver reacts to a potential hazard, and the braking distance is the distance the car travels while braking to a complete stop.

3. What is the average stopping distance for a car traveling at 60 mph?

The average stopping distance for a car traveling at 60 mph is approximately 240 feet. This includes an average thinking distance of 60 feet and an average braking distance of 180 feet.

4. How does speed affect the total stopping distance of a car?

The higher the speed of the car, the longer the total stopping distance will be. This is because as the speed increases, the thinking distance and braking distance also increase. It takes longer for the driver to react and for the car to come to a complete stop at higher speeds.

5. Can the total stopping distance of a car be reduced?

Yes, the total stopping distance of a car can be reduced by maintaining the car's brakes and tires in good condition, driving at a safe speed, and paying close attention to the road and potential hazards. In addition, keeping a safe distance between vehicles and avoiding distractions while driving can also help reduce the total stopping distance.

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