Kinematic Question -- Car braking to avoid hitting a fox

In summary, Andrew traveled 35.36 m before stopping. He did not hit the fox as he stopped 6.64 m in front of it. It took approximately 8 van lengths for Andrew to stop.
  • #1
Evangeline101
112
5

Homework Statement



Andrew is driving his van to deliver groceries in Elmvale. As he travels along Hwy 92, a fox stops on the road. Andrew is traveling at 75 km/h and is 42 m away from the fox when he applies his brakes. It takes him 3.4 s to stop.

a) How far did Andrew travel before stopping?

b) Did Andrew hit the fox? Explain your answer by including a calculation.

c) If a typical van is 4.2 m in length, how many van lengths did it take Andrew to stop?

Homework Equations


Δd = v2+v1/2 (Δt)

The Attempt at a Solution


[/B]
Given:
v1 = 75 km/h
convert 75 km/h to m/s = 20.8 m/s

Δd = 42 m

Δt = 3.4 s a) Δd = v2+v1/2 (Δt)
Δd = (0 m/s + 20.8 m/s) /2 x (3.4s)
Δd = 35.36 m

Andrew traveled 35.36 m before stopping.

b) 42 m - 35.36 m = 6.64 m
Andrew stopped 6.64 m in front of the fox and therefore did not hit it.

c) 35.36 m / 4.2 m = 8.4 van lengths
It took approximately 8 van lengths for Andrew to stop.

Please look over this and tell me if it is correct. Thanks :)
 
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  • #2
It all looks good.

The formula Δd = v2+v1/2 (Δt) should be written with parentheses in the numerator as Δd = (v2+v1)/2 (Δt) in order to indicate the proper order of operations.
 
Last edited:
  • #3
Ok, thanks for checking it out :)
 

What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the causes of motion.

What is the difference between speed and velocity?

Speed is the measure of how fast an object is moving, while velocity is the measure of both speed and direction of an object's motion.

How does a car's braking distance depend on its initial speed?

The braking distance of a car depends on its initial speed and the braking force applied to it. The higher the initial speed, the longer the braking distance will be.

What is the formula for calculating the braking distance of a car?

The formula for calculating the braking distance of a car is d = (v^2)/(2u), where d is the braking distance, v is the initial velocity, and u is the coefficient of friction between the tires and the road surface.

How does the weight of a car affect its braking distance?

The weight of a car affects its braking distance as a heavier car will require more force to stop, thus increasing the braking distance. This is because the larger mass of the car requires more energy to be dissipated in order to bring it to a stop.

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