Answer:
The person is moving at 5 meters per second (m/s)
The person has traveled 6 meters
Explanation:
This is an example of accelerated motion (motion under acceleration), and therefore we need to use the appropriate equations of motion for it.
The information we have includes:
1) The initial velocity ([tex]v_i[/tex]) of the person = 1 m/s
2) The person's acceleration ([tex]a[/tex]) = 2 [tex]m/s^2[/tex]
3) The time (t) the person moves under accelerated motion = 2 seconds
The following two equations are those to find the final velocity under accelerated motion, and the distance covered (from initial position [tex]x_i[/tex] to final position [tex]x_i[/tex]) under accelerated motion:
[tex]v_f=v_i+a*t\\x_f-x_i=v_i*t+\frac{1}{2} a*t^2[/tex]
We use the first equation and the information given, to find the speed of the person after 2 second under this motion:[tex]v_f=v_i+a*t\\v_f=1\frac{m}{s} +2\frac{m}{s^2} * 2s=(1+4)\frac{m}{s} = 5\frac{m}{s}[/tex]
We use the second formula to find the distance traveled by the person:
[tex]x_f-x_i=v_i*t+\frac{1}{2} a*t^2\\distance=1\frac{m}{s} * 2s+\frac{1}{2} 2*\frac{m}{s^2}*(2s)^2\\distance=2m+4m=6m[/tex]
