A particle moving along X-axis has acceleration f,at time t given by f=fₒ(1- t/T)

⇦

⇨

A particle moving along X-axis has acceleration f,at time t given by f=fₒ(1- t/T), where fₒ and T are constants. The particle’s velocity (vₓ) is

Options

(a) fₒT
(b) (1/2)fₒT²
(c) fₒT²
(d) (1/2)fₒT

Correct Answer:

(1/2)fₒT

Explanation:

Acceleration, f = dv/dt = f₀[1-(t/T)]
dv = f₀[1-(t/T)]dt —–(i)
On integrating Equation (i) both sides, we get
.·. v = f₀t – (f₀/T)(t²/2)dt + C —–(ii)
After applying boundery conditions v = 0 at t = 0, we get
Therefore, C = 0
v = f₀t – (f₀/T)(t²/2)dt —–(iii)
As, f = f₀[1-(t/T)]
When, f = 0,t = T
Substituting, t = T in Equation (iii), then velocity
vₓ = f₀T – (f₀/T)(T²/2)
= f₀T – (1/2)f₀T = (1/2)fₒT

Related Questions:

1. A particle of mass 1mg has the same wavelength as an electron moving with a velocity
2. Resistances n, each r Ω, when connected in parallel give an equivalent resistance
3. If 20% of a radiactive element decays in 10 days, then amount of original material left
4. An alpha nucleus of energy 1/2 mv² bombards a heavy nuclear target of charge Ze
5. A wire of length 1 m is moving at a speed of 2 ms⁻¹ perpendicular to its length

Topics: Motion in Straight Line (93)
Subject: Physics (2479)

---

Important MCQs Based on Medical Entrance Examinations To Improve Your NEET Score

18000+ students are using NEETLab to improve their score. What about you?

Solve Previous Year MCQs, Mock Tests, Topicwise Practice Tests, Identify Weak Topics, Formula Flash cards and much more is available in NEETLab Android App to improve your NEET score.

---

Share this page with your friends