A particle is moving with a constant velocity in the +x +
x
-direction. When the particle reaches the origin, a constant force is exerted on it in the +y
+
y
-direction. Which of the following graphs best shows the path the particle will follow?

The options are not shown, so i will answer in a general way:

We can separate the problem in two cases.

The movement in the x-axis, that is unperturbed, so the particle will keep moving in the +x direction with the same speed.

The movement in the y-axis, as a constant force is applied, by the second Newton's law:

F = m*a

a = F/m = constant

v = a*t + v0

p = (a/2)*t^2 + v0*t + p0

Where v0 = initial velocity in the y-axis, p0 = initial position (in this case the origin) and t is the time. (In this case, these values really do not matter, i only want to show the general equations of movement in the y-axis)

We will also have a constant acceleration, which means that the velocity in this axis will be linear, and the position quadratic, then after the particle reaches the origin, it will start moving up and to the right, and the upward movement will increase in magnitude as time passes, a graph in the x-y plane would be something like:

it is called kinetic energy