You are driving at the speed of 33.4 m/s
(74.7296 mph) when suddenly the car in
front of you (previously traveling at the same speed) brakes. Considering an average human reaction, you press your brakes 0.484 s later. Assume that the brakes on both cars are fully
engaged and that the coefficient of friction is 0.92 between both cars 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.
This problemn contains more information than necessary to answer the question. It may be they are trying to confuse you. Or uou may need the extra information in a followup question about whether you hit the car or not.
The deceleration of the car in front has nothing to do with your car or reaction time. It is
a = -F/m,
where F is the friction force and m is the mass. The minus sign indicates deceleration.
Although they do not tell you the mass, it will cancel out of the equation when you write
F = 0.92 m g
Thus a = -0.92 g
Well, it seems like you're in quite a pickle! Don't worry, I'll do my best to help you out with this physics problem. Let's break it down step by step!
First, let's calculate the deceleration of the car in front of you using the formula:
acceleration = (final velocity - initial velocity) / time
The initial velocity of the car in front of you is 33.4 m/s, and since the brakes are fully engaged, its final velocity would be 0 m/s. The time it takes for the car in front to come to a stop is 0.484 seconds. Plug these values into the formula:
acceleration = (0 - 33.4) / 0.484
Solving this, we get:
acceleration = -69.01 m/s^2
So, the acceleration of the car in front of you, when it brakes, is -69.01 m/s^2. The negative sign indicates that the car is decelerating.
Remember, it's always important to maintain a safe distance and be prepared for sudden stops from the car in front of you. And of course, always keep a smile on your face, even in traffic!
To calculate the acceleration of the car in front of you when it brakes, we can use the following steps:
Step 1: Calculate the deceleration of your own car.
Given:
Initial speed of your car, u1 = 33.4 m/s
Reaction time, t = 0.484 s
Acceleration due to gravity, g = 9.8 m/s^2
We need to find the deceleration of your car (negative acceleration since you are slowing down):
Using the formula: a = (v - u) / t
Here, v is the final velocity, and it is 0 m/s as your car comes to a stop.
Plugging in the values:
a1 = (0 - 33.4) / 0.484
Step 2: Calculate the deceleration of the car in front of you.
Given:
Coefficient of friction, μ = 0.92
We know that the frictional force acting on the car in front can be calculated as the product of its normal force and the coefficient of friction:
Frictional force = μ * Normal force
Since the car in front is also coming to a stop, the net force acting on it is zero.
The net force acting on the car in front is the sum of the frictional force and the gravitational force:
Net force = Frictional force + Weight of the car
The weight of the car is given by the formula: Weight = mass * acceleration due to gravity
The equation becomes:
0 = μ * Normal force + (mass * g)
We can rearrange this equation to solve for the deceleration of the car in front:
Deceleration = μ * g
Plug in the given values:
a2 = 0.92 * 9.8
Step 3: Solve for the acceleration of the car in front of you.
Given that the car in front and your car were initially traveling at the same speed, it means their decelerations are also the same:
a1 = a2
So, the acceleration of the car in front of you when it brakes is:
a2 = a1 = (0 - 33.4) / 0.484
Please input the values for the speed and reaction time to get the accurate calculation.
To calculate the acceleration of the car in front of you when it brakes, we can use the concept of deceleration.
1. First, let's calculate the initial velocity (u) of both cars:
- Your initial velocity (u1) is given as 33.4 m/s.
- The car in front of you also has the same initial velocity (u2) as they were previously traveling at the same speed.
2. Next, let's calculate the time taken for you to react and start braking:
- The time taken for you to press the brakes (t) is given as 0.484 seconds.
3. Now, we can calculate the deceleration (a) of your car:
- The deceleration can be calculated using the formula:
a = (v - u) / t,
where v is the final velocity, u is the initial velocity, and t is the time taken.
- As per the given information, your final velocity (v1) is 0 m/s (assuming you come to a complete stop).
- Substitute the values into the formula to find the deceleration (a1) of your car.
4. Since the coefficient of friction is mentioned, we can relate the deceleration of your car (a1) and the other car (a2):
- The deceleration is given by the formula:
a = μ * g,
where μ is the coefficient of friction and g is the acceleration due to gravity.
- The coefficient of friction (μ) is given as 0.92 in the question.
- The acceleration due to gravity (g) is given as 9.8 m/s^2.
- Since both cars experience the same coefficient of friction, the deceleration (a1) of your car and the other car (a2) will be the same.
5. Finally, use the calculated deceleration (a2) and the given initial velocity (u2) to find the final velocity (v2, when the car in front of you stops):
- Use the formula:
v2^2 = u2^2 + 2*a2*s,
where s is the distance covered during braking. Here, we are assuming that the car in front of you stops completely, so v2 is 0 m/s.
- Rearrange the formula to calculate a2, substituting the given values.
By following the above steps, you should be able to calculate the acceleration of the car in front of you when it brakes.