TargetIIT

Q. The position vector of a particle is given by the relation [im]http://codecogs.izyba.com/gif.latex?%5Cvec%7Br%7D%20%3D%20%5Cvec%7B%5Calpha%20%7D%281-%5Cgamma%20t+%5Cbeta%20t%5E%7B2%7D%29[/im], where [im]http://codecogs.izyba.com/gif.latex?%5Cvec%7B%5Calpha%20%7D[/im] is a constant vector while [im]http://codecogs.izyba.com/gif.latex?%5Cbeta[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Cgamma[/im] are positive constants. Which of the following statements is true?

(a) Velocity at t=0 is [im]http://codecogs.izyba.com/gif.latex?-%5Cgamma%20%5Cvec%7B%5Calpha%20%7D[/im]
(b) displacement in the first two seconds is [im]http://codecogs.izyba.com/gif.latex?%5Cvec%7B%5Calpha%20%7D%281-2%5Cgamma%20+4%5Cbeta%20%29[/im]
(c) Acceleration at t=0 is [im]http://codecogs.izyba.com/gif.latex?2%5Cbeta%20%5Cvec%7B%5Calpha%20%7D[/im]
(d) speed is decreasing with time at t=0

abc

@che: dont think b is true .. check again..

(d) is also true naa?

acceleration positive  at t=0 so speed is increasing at t=0

ya b is not correct..agree with u

yes asish....me gettin...abd...

b> says displacement not distance......

@che. acceleration positive.. direction of vel. is negative... so it serves as to decrease the speed naa?

position at t=2 is what is given in (b)

It is asking displacement.. which is r(2) - r(0)

a=d[p]2[/p]r/dt[p]2[/p] >0 at t=0

so v=dr/dt is an increasing at t=0

hence v is increaing at t=0

so speed is increasing

am i rong with it?

may be a fig will help

[image]43294314.jpg[/image]