Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
The relation between fuel consumption \( F \) (liters per 100 km) and speed \( V \) (km/h) under some constraints is given as:
\[ F = \frac{V^2}{500} - \frac{V}{4} + 14. \]
On the basis of the above information, answer the following questions:
(i) Find \( F \), when \( V = 40 \, \text{km/h} \).
(ii) Find \( \frac{dF}{dV} \).
(iii)(a) Find the speed \( V \) for which fuel consumption \( F \) is minimum.
OR
(b) Find the quantity of fuel required to travel \( 600 \, \text{km} \) at the speed \( V \) at which \( \frac{dF}{dV} = -0.01 \).
Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
The relation between fuel consumption \( F \) (liters per 100 km) and speed \( V \) (km/h) under some constraints is given as:
\[ F = \frac{V^2}{500} - \frac{V}{4} + 14. \]
On the basis of the above information, answer the following questions:
(i) Find \( F \), when \( V = 40 \, \text{km/h} \).
(ii) Find \( \frac{dF}{dV} \).
(iii)(a) Find the speed \( V \) for which fuel consumption \( F \) is minimum.
OR
(b) Find the quantity of fuel required to travel \( 600 \, \text{km} \) at the speed \( V \) at which \( \frac{dF}{dV} = -0.01 \).
Show Hint
Solution and Explanation
Substitute \( V = 40 \) into the formula: \[ F = \frac{V^2}{500} - \frac{V}{4} + 14. \] Simplify step-by-step: \[ F = \frac{40^2}{500} - \frac{40}{4} + 14, \] \[ F = \frac{1600}{500} - 10 + 14. \] Perform the calculations: \[ F = 3.2 - 10 + 14 = 7.2. \] Final Answer:
\[ \boxed{F = 7.2 \, \text{liters per 100 km.}} \]
Top Questions on Functions
- If \( f : \mathbb{R} \to \mathbb{R} \) and \( g : \mathbb{R} \to \mathbb{R} \) are two functions defined by \( f(x) = 2x - 3 \) and \( g(x) = 5x^2 - 2 \), then the least value of the function \((g \circ f)(x)\) is:
- Let \( f(x) = \frac{x - 5}{x^2 - 3x + 2} \). If the range of \( f(x) \) is \( (-\infty, \alpha) \cup (\beta, \infty) \), then \( \alpha^2 + \beta^2 \) equals to.
Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
On the basis of the given information, answer the followingIs \( f \) a bijective function?- Find $ k $ so that the function \[ f(x) = \begin{cases} \frac{x^2 - 2x - 3}{x + 1} & \text{if } x \neq -1 \\ k & \text{if } x = -1 \end{cases} \] is continuous at $ x = -1 $.
- Domain of $ \sin^{-1}(2x^2 - 3) $ is:
Questions Asked in CBSE CLASS XII exam
- In the circuit, three ideal cells of e.m.f. \( V \), \( V \), and \( 2V \) are connected to a resistor of resistance \( R \), a capacitor of capacitance \( C \), and another resistor of resistance \( 2R \) as shown in the figure. In the steady state, find (i) the potential difference between P and Q, (ii) the potential difference across capacitor C.
- CBSE CLASS XII - 2025
- Current electricity
- The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
- What type of cell is mercury cell? Why is it more advantageous than dry cell?
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Electrochemistry
A compound (A) with molecular formula $C_4H_9I$ which is a primary alkyl halide, reacts with alcoholic KOH to give compound (B). Compound (B) reacts with HI to give (C) which is an isomer of (A). When (A) reacts with Na metal in the presence of dry ether, it gives a compound (D), C8H18, which is different from the compound formed when n-butyl iodide reacts with sodium. Write the structures of A, (B), (C) and (D) when (A) reacts with alcoholic KOH.
- CBSE CLASS XII - 2025
- Haloalkanes And Haloarenes
- State Faraday’s second law of electrolysis. How much electricity is required in terms of Faraday for the reduction of 1 mole of $Cr_2\text{O}_7^{2-} \text{ to Cr}^{3+}$?
- CBSE CLASS XII - 2025
- Electrochemistry