Question

A student is skiing down a hill in a straight line, accelerating at a constant rate. she is displaced 10 m in 6 seconds and has a velocity of 20 m/s. what is the magnitude of her initial velocity?

Answer 1

Using kinematic equations and given values of displacement and final velocity, we can calculate the skier's constant acceleration and use that to determine the initial velocity.

Step-by-step explanation:

To find the skier's initial velocity, we can use the kinematic equations for uniformly accelerated motion. Since the skier is moving down a hill in a straight line and accelerating at a constant rate, we can apply the following equation:

s = ut + ( frac{1}{2} )at2

Where:

• s is the displacement (10 m)
• u is the initial velocity
• t is the time (6 seconds)
• a is the acceleration

We are also given that the final velocity v is 20 m/s after 6 seconds. To find the acceleration a, we can use another kinematic equation:

v = u + at

Substituting the known values:

20 m/s = u + a(6 s)

Since we don't have the value of acceleration a, we need another step to find it. We can rearrange the first equation:

10 m = 6u + 18a

Now we have two equations with two unknowns:

1. 20 m/s = u + 6a
2. 10 m = 6u + 18a

Solving this system of equations by substitution or elimination will give us the values of u (the initial velocity) and a (the acceleration). Once a is found, it can be substituted back into either equation to find u, the initial velocity of the skier.