Question

the coordinates of a moving particle at any time t are given by X=ct and y=bt. the speed of the particle at time t is given by

Answer 1

Vx= c and Vy = b ; we got by differentiating the above equations.
Using parallelogram law of vector addition,
speed = (c*2+ b*2)*1/2

Answer 2

Correct Question,

The coordinates of a moving particle at any time t are given by x = ct and y = bt². The speed of the particle is given by :-

Given :-

x = ct and y = bt².

Differentiating x w.r.t t in order to get velocity in horizontal direction.

Vx = dx/dt

Vx = d(ct)/dt

Vx = c

Again,

Differentiating y w.r.t t in order to get velocity in vertical direction.

Vy = dy/dt

Vy = d(bt²)/dt

Vy = 2bt (xⁿ = nxⁿ-¹)

We have velocity in both directions i.e. x and y direction. Hence, we will find resultant of Velocity.

|V| = √(Vx)² + (Vy)²

|V| = √(c)² + (2bt)²

|V| = √c² + 4b²t²

Hence,

The velocity of particle = |V| = √c² + 4b²t².