A particle's initial velocity is given by vox = -1.0 m/s and voy = 3.0 m/s. Its acceleration is ax = 0.50 m/s^2 and ay = -0.90 m/s^2 (a) Calculate its velocity 2.0 s later. (b) Calculate its displacement at that time.

I will be happy to critique your thinking.

Solve for velocity at 2.0s

vx = v0x + axt
vx = (-1m/s) + (0.5m/s2)(2.0s)
vx = 0m/s

vy = v0y + ayt
vx = (3m/s) + (-0.9m/s2)(2.0s)
vx = 1.2m/s

v = 0m/s(x hat) + 1.2m/s(y hat)

Calculate displacement.
∆x = v0xt + 1/2axt2
∆x = (-1m/s)(2.0s) + 1/2(0.5m/s2)(2.0s)2
∆x = -1m

∆y = v0xt + 1/2axt2
∆y = (3m/s)(2.0s) + 1/2(-0.9m/s2)(2.0s)2
∆y = 4.2m

y = -1.0m(x hat) + 4.2m(y hat)

To solve this problem, we can use the equations of motion. Let's break down the steps to find the answers to both parts (a) and (b):

(a) Calculate its velocity 2.0 s later:

Step 1: Start with the given initial velocity (vox, voy) and acceleration (ax, ay).

Given:
vox = -1.0 m/s (initial x velocity)
voy = 3.0 m/s (initial y velocity)
ax = 0.50 m/s^2 (x acceleration)
ay = -0.90 m/s^2 (y acceleration)
t = 2.0 s (time)

Step 2: Calculate the final velocity (vfx, vfy) in the x and y directions separately.

Use the equation:
vfx = vox + ax * t
vfy = voy + ay * t

Plugging in the values:
vfx = -1.0 m/s + 0.50 m/s^2 * 2.0 s
vfy = 3.0 m/s + -0.90 m/s^2 * 2.0 s

Calculating the values:
vfx = -1.0 m/s + 1.0 m/s = 0.0 m/s (final x velocity)
vfy = 3.0 m/s + -1.8 m/s = 1.2 m/s (final y velocity)

So, the velocity 2.0 s later is vfx = 0.0 m/s in the x direction and vfy = 1.2 m/s in the y direction.

(b) Calculate its displacement at that time:

Step 1: Start with the given initial velocity (vox, voy), acceleration (ax, ay), and time (t).

Given:
vox = -1.0 m/s (initial x velocity)
voy = 3.0 m/s (initial y velocity)
ax = 0.50 m/s^2 (x acceleration)
ay = -0.90 m/s^2 (y acceleration)
t = 2.0 s (time)

Step 2: Calculate the displacement (Sx, Sy) in the x and y directions separately.

Use the equation:
Sx = vox * t + (1/2) * ax * t^2
Sy = voy * t + (1/2) * ay * t^2

Plugging in the values:
Sx = -1.0 m/s * 2.0 s + (1/2) * 0.50 m/s^2 * (2.0 s)^2
Sy = 3.0 m/s * 2.0 s + (1/2) * -0.90 m/s^2 * (2.0 s)^2

Calculating the values:
Sx = -2.0 m + 0.5 m = -1.5 m (displacement in the x direction)
Sy = 6.0 m + -1.8 m = 4.2 m (displacement in the y direction)

So, the displacement at 2.0 s later is Sx = -1.5 m in the x direction and Sy = 4.2 m in the y direction.