A 8000N car is traveling 12 m/s along a horizntal road when the brakes are applied. The car skids to a stop in 4.0s. How much kinetic energy does the car have.

my work:

W= 8000N/9.18m/s
mass= 815.49 kg
Kinetic energy= (1/2mv^2-1/2mv^2)
kinetic energy=1/2 (815.49)(0)^2 - 1/2 (815.49)(12 m/s)^2 =5.0 X 10^4 J
Does this seem right

I think the issue is number of significant digits. Taking it to two, I get 5.8 If you use the 8000 as one sig digit, the answer is 6*10^4 J.

so I have the right idea

Bot Bot answered
1 year ago

but the wrong answer?

Step-by-Step Bot Step-by-Step Bot answered
9 months ago

Yes, you have the right idea. Your calculations are mostly correct. However, there seems to be a misunderstanding in your work when you calculated the work done by dividing 8000N by 9.18m/s. The unit for work is Joules (J), not Newtons per meter (N/m). So, the correct calculation for the work done would be:

Work (W) = force (F) × distance (d)
W = 8000N × 12m
W = 96000 J

To calculate the kinetic energy (KE) of the car, you can use the formula:

KE = (1/2) × mass (m) × velocity (v)^2
KE = (1/2) × 815.49kg × (12m/s)^2
KE = 58901.76 J

Rounded to two significant digits, the kinetic energy of the car is approximately 59000 J.

Explain Bot Explain Bot answered
9 months ago

It seems like you have the right idea in calculating the kinetic energy of the car. However, there are a few corrections and explanations that I can provide to further clarify the solution.

First, let's address the calculation of the car's mass. You mentioned using the formula W = mg, where W represents the weight of the car (8000 N) and g is the acceleration due to gravity (approximately 9.8 m/s^2). However, in this case, you should use the formula W = ma, where W is the net force acting on the car (8000 N), and a is the acceleration of the car.

Therefore, the equation becomes:
8000 N = ma

To solve for the mass (m), we need the value of acceleration. In this scenario, since the car is skidding to a stop, the acceleration is the deceleration due to the braking. To find the deceleration, we can use the formula v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (12 m/s), a is the deceleration, and t is the time taken to stop (4.0 s).

Using this equation, we rearrange to solve for deceleration (a):
0 m/s = 12 m/s + (a)(4.0 s)

Simplifying the equation, we have:
-12 m/s = 4.0s(a)

Therefore, the deceleration (a) becomes:
a = -12 m/s / 4.0 s
a = -3.0 m/s^2

Now, substituting this deceleration value (a) back into the equation to find the mass (m):
8000 N = m(-3.0 m/s^2)

To isolate the mass, we divide both sides of the equation by -3.0 m/s^2:
8000 N / -3.0 m/s^2 = m
m ≈ -2666.67 kg

Note that the negative sign indicates that the force and acceleration are in opposite directions.

Now that we have the correct mass of the car (approximately -2666.67 kg), we can calculate the kinetic energy using the formula:
Kinetic Energy = (1/2)mv^2

Plugging in the values:
Kinetic Energy = (1/2)(-2666.67 kg)(12 m/s)^2
Kinetic Energy ≈ 159999.96 J

Rounding to two significant digits, we would have:
Kinetic Energy ≈ 1.6 × 10^5 J

Therefore, the correct answer for the kinetic energy of the car is approximately 1.6 × 10^5 J.