Question

1) A particle move along the x axis, as x=tsquare-2t+1(SI unit). (a) The functions of its velocity and accelerator vector against time; (b) Its average velocity in the first 2 seconds

Answer 1

Answer:

$\text{I believe this is calculus, no? But I believe that there should be a y-component of position}\\\text{But based off of the information provided, here goes:}\\\text{(a)}\\x'(t)=v(t)=\frac{d}{dt}t^2-2t+1\\v(t)=2t-2\text{ is the velocity vector}\\v'(t)=a(t)=\frac{d}{dt}2t-2\\a(t)=2 \text{ is the acceleration vector}\\\text{(b)}\\\text{Average Velocity }=\frac{x_{f}-x{i}}{t_{f}-t_{i}}\\=\frac{1-1}{2}=0, \text{based off of the information provided, the average velocity in the first 2 seconds}: 0m/s$