What is the Velocity and Displacement of a Particle After 2.0s?

[chrisfnet]

Homework Statement

A particle's initial velocity is given by v_0x = -1.0m/s and v_0y = 3.0m/s; it's acceleration is a_x = 0.50m/s2 and a_y = -0.90m/s2. (a) Calculate its velocity 2.0s later. (b) Calculate its displacement at that time.

Homework Equations

v_x = v_0x + a_xt
∆x = v_0xt + 1/2a_xt²
∆y = v_0yt + 1/2a_yt²

The Attempt at a Solution

v = -1.0m/s(x hat) + 3.0m/s(y hat)
a = 0.5m/s²(x hat) - 0.9m/s²(y hat)

Solve for velocity at 2.0s
v_x = v_0x + a_xt
v_x = (-1m/s) + (0.5m/s²)(2.0s)
v_x = 0m/s

v_y = v_0y + a_yt
v_x = (3m/s) + (-0.9m/s²)(2.0s)
v_x = 1.2m/s

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

Calculate displacement.
∆x = v_0xt + 1/2a_xt²
∆x = (-1m/s)(2.0s) + 1/2(0.5m/s²)(2.0s)²
∆x = -1m

∆y = v_0xt + 1/2a_xt²
∆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)

 

[Redbelly98]

Looks good.