A force (3x² + 2x - 5) N displaces a body from x = 2 m to x = 4 m. Work done by this force is ________ J. Numerical answer type. Work it out, then open the answer.

Answer: 58. Variable force: W = ∫₂⁴ (3x² + 2x - 5) dx = [x³ + x² - 5x]₂⁴ = (64 + 16 - 20) - (8 + 4 - 10) = 60 - 2 Work done = 58 J.

A force (3x² + 2x - 5) N displaces a body from x = 2 m to x = 4 m… | JEE Main 2024 (9 Apr, Shift 2)

Q7JEE Main 2024 · 9 APR · SHIFT 2Easy

Work by a Constant Force

A force $(3x^2 + 2x - 5)\text{ N}$ displaces a body from $x = 2\text{ m}$ to $x = 4\text{ m}$ . Work done by this force is ________ J.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 58

Variable force: $W = \int_{2}^{4} (3x^2 + 2x - 5)\,dx = \left[x^3 + x^2 - 5x\right]_2^4$
$= (64 + 16 - 20) - (8 + 4 - 10) = 60 - 2$
Work done $= 58$ J.

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different…JEE Main 2024 (5 Apr, Shift 1)
A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the…JEE Main 2024 (29 Jan, Shift 1)
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60° by…JEE Main 2024 (30 Jan, Shift 2)
A small particle moves to position 5i - 2j + k from its initial position 2i + 3j - 4k…JEE Main 2023 (1 Feb, Shift 1)
Identify the correct statements from the following: A. Work done by a man in lifting a…JEE Main 2023 (29 Jan, Shift 2)
To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km…JEE Main 2023 (12 Apr, Shift 1)
Two persons A and B perform same amount of work in moving a body through a certain…JEE Main 2021 (27 Aug, Shift 1)
A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a…JEE Main 2021 (22 Jul, Shift 2)