A particle starts from origin at t = 0 with a velocity 5 i ^ m s - 1 and moves in x - y plane under action of a force which produces a constant acceleration of ( 3 i ^ + 2 j ^ ) m s - 2 . If the x -coordinate of the particle at that instant is 84 m , then the speed of the particle at this time is α m s - 1 . The value of α is _______.

Step-by-step solution

Given, u x = 5 m s - 1 , a x = 3 m s - 2 , x = 84 m The formula to calculate the velocity of the particle along x-axis is given by v x 2 = u x 2 + 2 a x . . . 1 From equation (1), it follows that v x 2 = 25 + 2 ( 3 ) ( 84 ) ⇒ v x = 23 m s - 1 Also, the velocity of the particle along x-axis can be written as v x = u x + a x t . . . 2 From equation (2), it follows that t = 23 - 5 3 = 6 s Similarly, for the y - component of the velocity, it follows that v y = 0 + a y t = 0 + 2 × ( 6 ) = 12 m s - 1 Hence, the magnitude