Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Motion in A Straight Line question

2007 · Q129
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /NEET
  3. /Physics
  4. /Motion in A Straight Line
  5. /2007 · Q129

Motion in A Straight Line question

2007 · Q129

NEETPhysicsMotion in A Straight LineMCQ+4 / −1
A particle moving along x-axis has acceleration f, at time t, given by f = f0(1−tT),\left( {1 - {t \over T}} \right),(1−Tt​), where f0 and T are constants.The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle's velocity (vx) is
  1. A
    12{1 \over 2}21​ f0T2
  2. B
    f0T2
  3. C
    12{1 \over 2}21​ f0T
  4. D
    f0T
View written solutionFree

Correct answer: C

f = f0(1−tT)\left( {1 - {t \over T}} \right)(1−Tt​)

When f = 0 then,

0 = f0(1−tT)\left( {1 - {t \over T}} \right)(1−Tt​)

⇒\Rightarrow⇒ (1−tT)\left( {1 - {t \over T}} \right)(1−Tt​) = 0

⇒\Rightarrow⇒ t = T

Also f = dvdt{{dv} \over {dt}}dtdv​

∴\therefore∴ ∫0vxdv=∫t=0t=Tfdt\int\limits_0^{{v_x}} {dv = \int\limits_{t = 0}^{t = T} {fdt} } 0∫vx​​dv=t=0∫t=T​fdt

vx = ∫t=0t=Tf0(1−tT)dt{\int\limits_{t = 0}^{t = T} {{f_0}\left( {1 - {t \over T}} \right)dt} }t=0∫t=T​f0​(1−Tt​)dt

= f0[(t−t22T)]0T{{f_0}\left[ {\left( {t - {{{t^2}} \over {2T}}} \right)} \right]_0^T}f0​[(t−2Tt2​)]0T​

= f0(T−T22T){{f_0}\left( {T - {{{T^2}} \over {2T}}} \right)}f0​(T−2TT2​)

= f0(T−T2){{f_0}\left( {T - {T \over 2}} \right)}f0​(T−2T​)

= 12{1 \over 2}21​ f0T

PreviousNext

More from Motion in A Straight Line

  • A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is2007 · MCQ
  • The positions x of a particle with respect to time t along x-axis is given by x = 9t2 − t3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?2007 · MCQ
  • Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is2006 · MCQ
  • A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t − t3. How long would the particle travel before coming to rest ?2006 · MCQ
  • A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is2006 · MCQ
  • A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise? (Take g = 10 m/s2.)2005 · MCQ
  • The displacement x of a particle varies with time t as x = ae−at + beβt, where a, b, α and β are positive constants. The velocity of the particle will2005 · MCQ
  • A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time ? (Given g = 9.8 m/s2)2003 · MCQ