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

A Particle Moving Along Xaxis Has Acceleration Fat Time T Physics Question

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. The valence band and the conductance band of a solid overlap at low temperature
  2. A particle covers half of its total distance with speed v1 and the rest half distance
  3. The optical path of a monochromatic light is same if it goes through 4.0 cm
  4. A susceptibility of a certain magnetic material is 400. What is the class
  5. An electric lamp is connected to 220 V, 50 Hz supply. Then the peak voltge is

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.

NEETLab Mobile App

Share this page with your friends

Be the first to comment

Leave a Reply

Your email address will not be published.


*