Question

Please solve this question

Answer 1

$x = 5t \\ y = 2 {t}^{2} + t$
Velocity of the particle will be along the tangent of the path at any time instant.

so, at any time instant (t) :

slope of tangent to the curve = dy/dx = (dy/dt) / (dx/dt)

dy/dt = 4t + 1
dx/dt = 5

dy/dx = (4t + 1) / 5

slope of the tangent at t = tan(45°) = 1


hence,

dy/dx = (4t + 1) / 5 = 1

=> 4t = 5 - 1 = 4
=> t = 1

so, required time = 1 sec ..