You are driving at the speed of 31 m/s
(69.3599 mph) when suddenly the car in
front of you (previously traveling at the same
speed) brakes and begins to slow down with
the largest deceleration possible without skidding. Considering an average human reaction,
you press your brakes 0.546 s later. You also
brake and decelerate as rapidly as possible
without skidding. Assume that the coefficient
of static friction is 0.925 between both carsβ
wheels and the road.
The acceleration of gravity is 9.8 m/s2.
Calculate the acceleration of the car in front
of you when it brakes.
Answer in units of m/s2
M*g = M*9.8 = 9.8M = Wt. of car.
Fp = 9.8M*sin 0 = 0 = Force parallel with surface.
Fn = 9.8M*Cos 0 = 9.8M = Normal force.
Fs = u*Fn = 0.925*9.8M = 9.1M. = Force of static friction.
Fp-Fs = M*a;
0-9.1M = M*a,
Divide both sides by M:
a = -9.1 m/s^2.
Well, well, well, we have got ourselves a braking race here. It's like the Fast and the Furious, but with a touch of physics! Let's dive into it.
To find the acceleration of the car in front when it brakes, we'll have to use some good old kinematics. We'll start by finding out how much distance the car in front travels during your reaction time.
Using the formula: π = π£0π‘ + (1/2)ππ‘^2, where π£0 is the initial velocity, π is the acceleration, and t is the time, we plug in the values.
Since both cars were traveling at 31 m/s, the initial velocity π£0 would be 31 m/s as well. The time π‘ would be your reaction time of 0.546 s. Now, since you were just chilling, enjoying the ride before braking, we can say your initial velocity π£0 is 31 m/s as well.
Putting it all together, we have π = 31(0.546) + (1/2)π(0.546)^2. Solving this equation will give us the distance traveled by the car in front during your reaction time.
Now, let's move on to finding out the maximum deceleration possible without skidding. We can calculate this using the coefficient of static friction. The maximum deceleration is given by πmax = ππ, where π is the coefficient of static friction and π is the acceleration due to gravity.
With π = 0.925 and π = 9.8 m/s^2, we can calculate the maximum deceleration πmax.
Finally, we can determine the acceleration of the car in front by dividing the distance traveled during your reaction time by the time it took to travel that distance.
So, put on your physics helmet and calculate away! Don't forget to carry the decimal clownfish!
(Note: My response is for humor purposes only. For an accurate calculation, please refer to a trusted source or consult an expert.)
To calculate the acceleration of the car in front of you when it brakes, we can use the equations of motion.
First, let's calculate the distance covered by the car in front of you during your reaction time of 0.546 s. We can use the equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
The initial velocity of the car in front of you is 31 m/s, and the time is 0.546 s. Since the car is decelerating (negative acceleration), we can assume the initial velocity is positive and the acceleration is negative. Let's denote the deceleration as "a" (negative):
distance = 31 m/s * 0.546 s + (1/2) * (-a) * (0.546 s)^2
Next, let's calculate the stopping distance of the car in front of you. We can use the equation for stopping distance:
stopping distance = (initial velocity)^2 / (2 * deceleration)
The initial velocity is 31 m/s, and the deceleration is the largest possible without skidding. We can calculate this deceleration using the coefficient of static friction between the wheels and the road. The formula for maximum deceleration without skidding is:
deceleration = coefficient of static friction * acceleration due to gravity
The coefficient of static friction is 0.925, and the acceleration due to gravity is 9.8 m/s^2. Plugging these values into the equation, we can find the deceleration.
Finally, the acceleration of the car in front of you when it brakes can be calculated by assuming the stopping distance is equal to the sum of the distance traveled during your reaction time (calculated earlier) and the stopping distance of the car in front of you:
stopping distance = distance + stopping distance
Rearranging this equation, we can find the acceleration "a" of the car in front of you.
Use these explanations to calculate the acceleration of the car in front of you when it brakes.
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