Question

A particle 9f mass m is ar test at the origin at time t = 0 . it is subjected to a force f(t) = F₀e⁻ᵇᵗ in the direction . it's speed v(t) is depicted by which of the following curve .

Option is given in attachment .
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Answer 1

Explanation:-As the force is exponentially decreasing , so its acceleration , i.e ,rate of increase of velocity will decrease with time . thus ,the graph of velocity will be an increasing curl with decreasing slope with time .

• ∴ a = F/M = F₀e⁻ᵇᵗ/m = dv/dt
• => ₀∫ᵛdv = ₀∫ᵗF₀e⁻ᵇᵗ/m dt
• v = F₀/m [ (1/-b) e⁻ᵇᵗ]₀ᵗ
• = F₀[e⁻ᵇᵗ]ₜᵒ/mb
• F₀/mb(e⁰-e⁻ᵇᵗ)
• F₀/mb(1-e⁻ᵇᵗ)
• Vᵐᵃˣ = F₀/mb

Since option (c) is correct option

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Answer 2

Answer:

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Option c is correct....

$\huge\boxed{\fcolorbox{red}{orange}{Explanation:}}$

As the force is exponentially decreasing, so its acceleration,i.e.rate.of increase of velocity will decrease with time,thus the graph of velocity will be increasing curl with decreasing slope with time...

As all this were shown in option c that us why it is correct..