The displacement `x` of particle moving in one dimension, under the action of a constant force is related to the time `t` by the equation ` t = sqrt(x) +3` where `x is in meters and t in seconds` . Find (i) The displacement of the particle when its velocity is zero , and (ii) The work done by the force in the first ` 6 seconds`.
Text Solution
Verified by Experts
As `t=sqrtx+3` i.e. `x=(t-3)^2` …(i) So, `v=(dx//dt)=2(t-3)` …(i) (a) v will be zero when `2(t-3)=0` i. e. `t=3` Substituting this value of t in Eq. (i), `x=(3-3)^2=0` i.e. when velocity is zero, displacement is also zero. (b) From Eq. (ii), `(v)_(t=0)=2(0-3)=-6m//s` and `(v)_(t=6)=2(6-3)=6m//s` So, from work-energy theorem `w=DeltaKE=1/2m[v_f^2-v_i^2]=1/2m[6^2-(-6)^2]=0` i.e. work done by the force in the first 6 s is zero.
Topper's Solved these Questions
WORK, ENERGY & POWER
DC PANDEY|Exercise Solved Examples|12 Videos
WORK, ENERGY & POWER
DC PANDEY|Exercise TYPE2|1 Videos
WAVE MOTION
DC PANDEY|Exercise Integer Type Question|11 Videos
WORK, ENERGY AND POWER
DC PANDEY|Exercise MEDICAL ENTRACES GALLERY|33 Videos
Similar Questions
Explore conceptually related problems
The distance x of a particle moving in one dimensions, under the action of a constant force is related to time t by the equation, t=sqrt(x)+3 , where x is in metres and t in seconds. Find the displacement of the particle when its velocity is zero.
The displacement x of a particle moving in one dimension under the action of a constant force is related to time t by the equation t=sqrt(x)+3 , where x is in meter and t is in second. Find the displacement of the particle when its velocity is zero.
The displacement x of a particle moving in one dismension under the action of a constant force is frlated to time t by the equation tsqrtx+3 , where x is in merers and t is in seconds, Find the displacemect of the particle when its velocity is zero.
The distance (x) particle moving in one dismension, under the action of a constant force is related to time (t) by equation tsqrt x +3 where (x) is in vettres and (t) in seconds. Find the displacement of the particle when its velcity is zero.
The displacement x of a particle of mass 1.0 kg moving the one dimension under the action of a force is related to time t by the equation t=sqrt(x)+5 where x is in meter and t is in second. The magnitude of the momentum of the particle
The displacement x of a particle of mass m kg moving in one dimension, under the action of a force, is related to the time t by the equation t=4x+3 where x is in meters and t is in seconds. The work done by the force in the first six seconds in joules is
The displacement x in meters of a particle of mass m kg moving in one dimension under the action of a force is related to the time t in seconds by the equation t=sqrtx+3 , , the work done by the force (in J) in first six seconds is :-
The displacement x in meter of a particle of mass mkg moving in one dimenstion under the action of a force is related to the time t in second by the equation x=(t-3)^2 . The work done by the force (in joules) in first six seconds is
The motion of a particle along a straight line is described by equation : x = 8 + 12 t - t^3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is.
DC PANDEY-WORK, ENERGY & POWER-Level 2 Comprehension Based
