a roller coaster, traveling with an initial speed of 15 meters per second, decelerates uniformly at -7.0 meters per second Squared to a full stop. Approximately how far does the roller coaster travel during its deceleration?
16m
To calculate the distance traveled during deceleration, we can use the following kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the roller coaster comes to a stop)
u = initial velocity (15 m/s)
a = acceleration (-7.0 m/s^2)
s = distance
Rearranging the equation, we can solve for s:
s = (v^2 - u^2) / (2a)
Substituting the given values, we get:
s = (0^2 - 15^2) / (2(-7.0))
Simplifying further, we have:
s = (-225) / (-14)
s = 16.07 meters
Therefore, the roller coaster travels approximately 16.07 meters during its deceleration.
To calculate the distance traveled by the roller coaster during deceleration, we need to use the equation:
distance = (initial speed)^2 / (2 * acceleration)
Given:
Initial speed (u) = 15 m/s
Acceleration (a) = -7.0 m/s^2
Plugging in the values into the formula, we get:
distance = (15 m/s)^2 / (2 * -7.0 m/s^2)
Simplifying the equation:
distance = 225 m^2/s^2 / (-14.0 m/s^2)
The square seconds cancel out, giving us:
distance = 225 m / (-14.0)
Calculating the value:
distance ≈ -16.07 m
The roller coaster travels approximately 16.07 meters during its deceleration. Note that the negative sign indicates direction, so the distance is considered "negative" since the coaster is moving in the opposite direction of the initial velocity.
The time it takes to stop is
Vo/a = 15/7 = 2.143 s
The average speed while stopping is
Vo/2 = 7.5 m/s
Multiply those two numbers to get the distance traveled while decelerating.