a hockey player skating at 19 m/s comes to a complete stop in 2.3 m. what is the acceleration of the hockey player?
To find the acceleration of the hockey player, we can use the formula:
acceleration (a) = (final velocity - initial velocity) / time
The initial velocity of the hockey player is 19 m/s, and since the player comes to a complete stop, the final velocity is 0 m/s. The time taken to come to a stop is not given in the question, so we'll need to use the given distance to calculate it.
We can use the equation of motion:
distance (d) = (initial velocity * time) + (0.5 * acceleration * time^2)
Rearranging this equation, we get:
acceleration (a) = (distance - initial velocity * time) / (0.5 * time^2)
Substituting the given values, we have:
distance = 2.3 m
initial velocity = 19 m/s
To find the time, we need to solve the equation for time:
2.3 = (19 * t) + (0.5 * a * t^2)
This is a quadratic equation, but since our unknown is time, we can solve this using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 0.5 * a, b = 19, and c = -2.3.
By substituting these values into the equation and solving for time, we can then find the value of acceleration by substituting the known values into the acceleration formula:
a = (0 - 19) / time
So, to summarize, follow these steps to find the acceleration:
1. Solve the quadratic equation to find the time taken to come to a stop.
2. Substitute the obtained time into the formula for acceleration.
By performing these calculations, you will find the acceleration of the hockey player.