Q1 THE COORDINATES OF A MOVING PARTICLE AT A TIME T, ARE GIVEN BY X=5SIN10T ,Y=5COS10T. THE SPEED OF THE PARTICLE ISQ2 A PARTICLES STARTS MOVING RECTILINARLY AT TIME ,T=O SUCH THAT ITS VELOCITY CHANGES WITH TIME T ACCORDING TO THE EQUATION V=T2-T WHERE TIS IN SECONDS &IS IN M\\SEC. THE TIME INTERVAL FOR WHICH PARTICLE RETARDS IST<1/2T.>11/2< T<1T=1

Hi

Ans 1 :Find the velocity in each direction seperately:

for X direction V_x= ðx/ðt = 5x10cos10T

for Y direction V_y = ðy/ðt = 5 x 10 ( - sin10T)

For calculating speed , we need to calculate ( V_x² + V_y²)^1/2 .

Hence answer is 50.

Ans 2:

Find the expression for acceleration by differentiating the velocity term given, ðv/ðT= 2T -1

For particle to retard acceleration should be less than 0, therefore 2T-1< 0 , hence T<1/2 is the answer.

Q1.

ans.       vx=5sin10t

               vy=scos10t

      v=[vx*vx+vy*vy]1/2

=5*10[sin2+cos2]1/2

=5*10[1]1/2

=5o