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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
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Topics: Motion in Straight Line
(93)
Subject: Physics
(2479)
Important MCQs Based on Medical Entrance Examinations To Improve Your NEET Score
- A car moving with a speed of 50 kmh⁻¹ can be stopped by brakes after at least 6 m
- If the focal length of a concave mirror is 50 cm, then where should the object
- A 0.01 H inductor and √3 πΩ resistance are connected in series
- Thin uniform rod of length L, cross-sectional area A and density ρ is rotated
- The fossil bone has a ¹⁴C:¹²C ratio, which is [1/16] of that in a living animal
Topics: Motion in Straight Line (93)
Subject: Physics (2479)
Important MCQs Based on Medical Entrance Examinations To Improve Your NEET Score
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