Question

What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 8.0 m/s when going down a slope for 5.0s and how far does the skier travel in this time?

Answer 1

Acceleration: `1.6 "m"/("s"^2)`

Distance: `20. "m"`

Explanation:

We can use the equation

`v_x = v_(0x) + a_xt`

To find the acceleration, assuming it's constant, of this motion. The initial velocity `v_(0x)` is `0`, as it started from rest. Thus, the acceleration is

`a_x = (v_(x))/t = (8.0 "m"/"s")/(5"s") = color(red)(1.6 "m"/("s"^2)`

Now, to find the distance `Deltax` the skier travels, we'll use the equation

`Deltax` = `v_(0x)t + 1/2a_xt^2`

Plugging in known variables, the distance `Deltax` the skier traveled is

`Deltax = (0)(5.0 "s") + 1/2(1.6"m"/("s"^2))(5.0"s")^2 = color(blue)(20. "m"`