A particle starts with the velocity u and moves in a straight line, its acceleration being always equl to its displacement. If v be the velocity when its desplacement is x, then show that `v^2=u^2+x^2`.

A particle starts with the velocity u and moves in a straight line, its acceleration being always equal to its displacement. If v be the velocity when its displacement is x, then show that v^2= u^2+x^2 .

A particle starts with the veloctiy u and moves in a straight line, its acceleration being always equal to its displacement. If v be the velocity when its displacement is x, the show that v^(2)=u^(2)+x^(2) .

A particle starts from the origin with a velocity 5 cm/s and moves in a straight line its accelration at time t seconds being (3t^(2)-5t)cm//s^(2) . Find the velocity of the particle and its distance from the origin at the end of 4 seconds.

A particle starts form the origin with a velocity of 10 cm/s and moves along a straight line. If its acceleration be (2t^(2)-3t)cm//s^(2) at the end of t seconds, then fing its velocity and the distance from the origin at the end of 6 seconds.

A particle moves along a straight line with a retardations of av^(n+1) , where v is the velocity at time t and a is a positive constant. If at t = 0 the velocity of the particle is u, show that at = (1)/(n)((1)/(v^(n))-(1)/(u^(n))).

A particle is moving in a straight line such that its retardation is directly proportional to its displacement . Decrease in the kinetic energy of the body is directly proportional to

A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the 4th second compared to that in the 3rd second is

A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the 4^(th) second compared to that in the 3 second is

A particle starting from a point A and moving with a positive constant acceleration along a straight line reaches another point B is time T. Suppose that the initial velocity of the particle is u gt0 and P is the midpoint of the line AB. If the velocity of the particle at point P is v_(1) and if the velocity at time (T)/(2) is v_(2) , then -