Question

A skateboarder coasts down a very tall hill. The skateboarder starts from rest at the top of the hill. After 3 seconds, her speed is 6 m/s. Assuming a constant slope, what is the acceleration of the skateboarder? How fast will the skateboarder be travelling after 8 seconds? Why does the hill have to have a constant slope to answer this question?

Answer 1

Here we know that skateboarder starts from rest

so we will have final speed 6 m/s after t = 3 s

so now we can use kinematics equation here

$v_f = v_i + at$

$6 = 0 + a(3)$

$a = 2 m/s^2$

Now we need to find the speed after t = 8 s

now we will again use same kinematic equation

$v_f = v_i + at$

$v_f = 0 + (2)(8)$

$v_f = 16 m/s$

So after t = 8 s speed must be 16 m/s

SO here we have constant slope given in the question so that we will have the situation of constant acceleration as we know that acceleration depends on the slope and hence we can use kinematics here