Question

The position of a particle is x - y plane is described by the variables x = at³ and y = 2at. Then the acceleration of the particle ______.

Options

• is 6a at t = 0

• is 6a at t = 1

• is 3a at t = 0

• is 3a at t = 1

Answer 1

The position of a particle is x - y plane is described by the variables x = at³ and y = 2at. Then the acceleration of the particle is 6a at t = 1.

Explanation:

Given that:

x = at³ ⇒ v_x = `("d"x)/("d"t)` = 3at²  ⇒ a_x = `("d"v_x)/("d"x)` = 6at

and y = 2at ⇒ v_y = `("d"y)/("d"t)` = 2a ⇒ a_y = `("d"v_y)/("d"t)` = 0.

∴ a² = `"a"_x^2 +"a"_y^2`

⇒ a = a_x (∴ a_y = 0)

∴ a = 6at

a = 6a, at t = 1s