What is the minimum stopping distance for a car traveling at a speed of 40 m/s?

In summary, the minimum stopping distance for a car traveling at a speed of 40 m/s is 100 m, including the distance traveled during the driver's reaction time of 0.50 s. The calculation for acceleration using the second equation is incorrect due to an error in determining the stopping time during acceleration.
  • #1
habibclan
55
0
Kinematics-- Stopping distance

Homework Statement



The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the driver's reaction time of 0.50 s. What is the minimum stopping distance for the same car traveling at a speed of 40 m/s?

Homework Equations



vf^2 = vi^2 + 2ad

a = (delta v)/ (delta t)


The Attempt at a Solution



Since the reaction time is 0.5 s, the distance traveled is 40 x 0.5= 20 m. Now, to find the time it takes to decrease the velocity to 0 m/s, one needs to find the acceleration whcih can be calculated in two ways and can someone please explain to me why the first way is incorrect!

Calculate Acceleration:
1) use equation

vf^2 = vi^2 + 2ad

I use the data for the initial velocity (first scenario) 30 m/s and the stopping distance 60 m, plug it into the eequation and i get -10 m/s^2. When I use this acceleration, vf (0 m/s) and vi (40 m/s) I can calculate d=80 m, which i add to the 20 m which it takes to react and the answer I get is 100 m.

1) However, if i use the equation, in which delta t= 2s - 0.5 s = 1.5 s. I subtracted the reaction time, the acceleration I get is a= (delta v)/(delta t) = (-40)/ (1.5) = -20 m/s^2. This acceleration is different from the acceleration calculated using the first equation. Can someone please tell me why this method is incorrect?

Thanks a lot!
 
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  • #2
habibclan said:
However, if i use the equation, in which delta t= 2s - 0.5 s = 1.5 s. I subtracted the reaction time, the acceleration I get is a= (delta v)/(delta t) = (-40)/ (1.5) = -20 m/s^2. This acceleration is different from the acceleration calculated using the first equation. Can someone please tell me why this method is incorrect?

Thanks a lot!
you've gone wrong here with your statement that delta t = 2s.
Where did this come from? If you are attempting to calculate the stopping time during acceleration in the first part of the problem, which itself is not correct, you should also note that the stop time during acceleration in the second part is not the same.
 
  • #3
Oh right. That delta 2 was a stupid mistake as I divide the initial velocity by the distance to get 2 s :S which was just out of habit. Thanks for the correction! I get it now!
 

Related to What is the minimum stopping distance for a car traveling at a speed of 40 m/s?

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It deals with the concepts of displacement, velocity, acceleration, and time.

2. What is stopping distance?

Stopping distance is the total distance a moving object travels from the moment the brakes are applied until it comes to a complete stop. It includes both the distance covered during the reaction time of the driver and the distance covered while the brakes are being applied.

3. How is stopping distance calculated?

Stopping distance is calculated using the equation: Stopping distance = reaction distance + braking distance. The reaction distance is the distance covered during the driver's reaction time, which is usually taken as 0.75 seconds. The braking distance is calculated using the equation: Braking distance = initial velocity² / (2 x deceleration). The deceleration is the negative acceleration due to braking.

4. What factors affect stopping distance?

The factors that affect stopping distance include the initial velocity of the object, the mass of the object, the coefficient of friction between the object and the surface it is moving on, and the reaction time of the driver. Other factors such as road conditions, weather, and tire conditions can also affect stopping distance.

5. How can stopping distance be reduced?

Stopping distance can be reduced by increasing the coefficient of friction between the object and the surface it is moving on, improving the braking system of the object, and reducing the initial velocity. Drivers can also reduce their reaction time by staying alert and focused while driving, and maintaining a safe distance from other vehicles on the road.

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