Question

A person wax walk at 1m/sand then accelerate at 2 m/s^2 for 2 seconds

After theses two seconds the person is moving at M/s and has traveled

Answer 1

The person is moving at 5 meters per second (m/s)

The person has traveled 6 meters

Step-by-step 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 (
`v_i`) of the person = 1 m/s

2) The person's acceleration (
`a`) = 2
`m/s^2`

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
`x_i` to final position
`x_i`) under accelerated motion:

`v_f=v_i+a*t\\x_f-x_i=v_i*t+(1)/(2) a*t^2`

We use the first equation and the information given, to find the speed of the person after 2 second under this motion:
`v_f=v_i+a*t\\v_f=1(m)/(s) +2(m)/(s^2) * 2s=(1+4)(m)/(s) = 5(m)/(s)`

We use the second formula to find the distance traveled by the person:

`x_f-x_i=v_i*t+(1)/(2) a*t^2\\distance=1(m)/(s) * 2s+(1)/(2) 2*(m)/(s^2)*(2s)^2\\distance=2m+4m=6m`