A particle moving in the xy plane experiences a velocity dependent force F⃗ = k(v_yı̂ + vₓȷ̂), where vₓ and v_y are the x and y components of its velocity v⃗. If a⃗ is the acceleration of the particle, then which of the following statements is true for the particle?

Question

Accepted Answer

(1) Quantity v⃗ × a⃗ is constant in time.. ma⃗ = F⃗; F⃗ · v⃗ = 2kvₓv_y 
eq 0, so not magnetic and kinetic energy changes. v⃗ × a⃗ = k/m(vₓ² - v_y²)k̂. d/(dt)(vₓ² - v_y²) = 2vₓ(kv_y)/m - 2v_y(kvₓ)/m = 0. So v⃗ × a⃗ is constant.

A particle moving in the xy plane experiences a velocity dependent force F⃗ = k(v_yı̂ + vₓȷ̂), where vₓ and v_y are the x and y components of its velocity v⃗. If a⃗ is the acceleration of the particle, then which of the following statements is true for the particle?

Step-by-step solution

Why the other options are wrong