If the time taken by a particle moving at constant acceleration to travel equal distances along a straight line are `t_(1), t_(2), t_(3)` respectively prove that `(1)/(t_(1))-(1)/(t_(2))+(1)/(t_(3))=(3)/(t_(1)+t_(2)+t_(3))`.

A partical traveIIing with uniform acceleration along a straight line has average velocities v_(1),v_(2) and v_(3) in successive time intervals t_(1),t_(2) and t_(3) respectively . Prove that, (v_(2)-v_(1))/(v_(3)-v_(2))=(t_(1)+t_(2))/(t_(2)+t_(3))

A particle crosses points A, B, C in a straight line at a constant acceleration. The particle travels from A to B in time t_(1) and B to C in time t_(2) . If AB = a , BC = b then prove that the acceleration of the particle is 2(bt_(1)-at_(2))//t_(1)t_(2)(t_(1)+t_(2)) .

A particle moves with uniform acceleration and the distance travelled in t - th second is s_(t) = 3 + 2t . Find the initial velocity of the particle .

Establish gas equation, (P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2)) .

If the normal at (at_(1)^(2),2at_(1)) "to" y^(2)=4ax intesect the parabola at (at_(2)^(2),2at_(2)) "then" t_(1)+t_(2)+(k)/(t_(1))=0 (t_(1) ne 0) , find k.

The base of a triangle is divided into three equal parts. If t_1, t_2,t_3 are the tangents of the angles subtended by these parts at the opposite vertex, prove that (1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/(t2 2))dot

Starting from the rest, an electron of mass m_(e) and a proton of mass m_(p) travel through a certain distance in a uniform electric field in times t_(1) and t_(2) , respectively. Find out the ratio t_(2)//t_(1) , neglecting the influence of gravity.

If the normal at (at_(1)^(2), 2at_(1))" to " y^(2) =4ax intersect the parabola at (at_(2)^(2), 2at_(2)) , prove that, t_(1)+t_(2)+(2)/(t_1)=0(t_(1) ne 0)

Under similar conditions of temperature and pressures, if the time taken for effusion of the same volume of H_(2),N_(2) and CO_(2) gas through the same porour wall are t_(1),t_(2) and t_(3) respectively, then arrange t_(1),t_(2) and t_(3) in their increasing order.

If the normals at P(t_(1))andQ(t_(2)) on the parabola meet on the same parabola, then (A) t_(1)t_(2)=-1 (B) t_(2)=-t_(1)-(2)/(t_(1)) (C) t_(1)t_(2)=1 (D) t_(1)t_(2)=2