PLEASE HELP
a skier crosses a 100m flat section past the chair lift at a constant velocity of 6m/s, then accelerates downhill at a rate of 0.5m/s^2 until reaching a maximum velocity of 12m/s.
a) how long did it take them to speed up?
b) if the skier maintains the 12m/s speed for an additional 20s to the bottom of the hill, what is the total displacement of the skier after they got off the chairlift?

a) t =12[s]; b) x = 348[m]

Explanation:

We can solve this problem using the following kinematics equations:

a)

where:

vf = final velocity = 12 [m/s]

vo= initial velocity = 6 [m/s]

a = acceleration = 0.5[m/s^2]

t = time [s]

Now clearing the time t, we have:

b)

We can calculate the displacement for the first 12 [s] then using the equation for the constant velocity we can calculate the other displacement for the 20[s].

The we can calculate the second displacement for the constant velocity:

x = x1 + x2

x = 108 + 240

x = 348[m]