Starting at time t = 0 from the origin with speed 1   m   s - 1 , a particle follows a two-dimensional trajectory in the x - y plane so that its coordinates are related by the equation y = x 2 2 . The x and y components of its acceleration are denoted by a x and a y , respectively. Then
D. a x = 0 implies that at t = 1 s , the angle between the particle's velocity and the x axis is 45 °
y = x 2 2 d y d t = 1 2 × 2 x d x d t v y = x v x d v y d t = d x d t × d x d t + x d 2 v x d t 2 a y = v x 2 + x a x If x = 0 , a y = v x 2 = 1 , No matters what is the value of a x hence, Option A is correct. If a x = 0 then x = v x t = t at t = 1 ; x = 1 m then angle made by velocity vector with x -axis tan θ = v y v x = x = 1 ⇒ θ = 45 °
Related: Physics — Motion In One Dimension · All PYQ Banks