Question

The maximum power of a car is given by

P = V³b
Where V is the velocity and b is a constant
P = 84Kw ± 5% and b = 0.56 ± 7%
Calculate the value of V and the absolute uncertainty in V.

Answer 1

The velocity V of the car is approximately 5.35 m/s, with an absolute uncertainty of 0.642 m/s, when the maximum power is 84 kW with 5% uncertainty and b is 0.56 with 7% uncertainty.

Step-by-step explanation:

To calculate the velocity V of the car when the maximum power P is given as 84 kW ± 5% and b is a constant with a value of 0.56 ± 7%, we first need to rearrange the equation P = V³b to solve for V:

V = ∛(P / b)

First, we'll calculate the values using the central value of P and b:

V = ∛(84 kW / 0.56) = ∛(150) ≈ 5.35 m/s

Next, we need to calculate the absolute uncertainty in V. Since V is directly proportional to P and inversely proportional to b, we can add the relative uncertainties:

Relative uncertainty in P = 5%
Relative uncertainty in b = 7%
Relative uncertainty in V = 5% + 7% = 12%

To find the absolute uncertainty in V, we multiply the relative uncertainty by the velocity:

Absolute uncertainty in V = 0.12 * 5.35 m/s ≈ 0.642 m/s

Therefore, the velocity of the car is approximately 5.35 m/s with an absolute uncertainty of 0.642 m/s.