If a cyclist traveling at 14.0m/s skids to a stop in 5.60 s, determine the skidding distance assume uniform acceleration?
Answer is 39.2m
To determine the skidding distance of the cyclist, we can use the kinematic equation:
d = v0 * t + (1/2) * a * t^2
Where:
d = skidding distance
v0 = initial velocity = 14.0 m/s
t = time taken to skid to a stop = 5.60 s
a = acceleration (which is assumed to be uniform)
To find the skidding distance, we need to calculate the acceleration. Since the cyclist comes to a stop, the final velocity (vf) is 0 m/s.
We can use the equation:
vf = v0 + a * t
Rearranging the equation to solve for acceleration:
a = (vf - v0) / t
= (0 - 14.0) / 5.60
= -14.0 / 5.60
= -2.50 m/s^2
Note that the negative sign indicates deceleration (opposite to the direction of motion).
Now, we can substitute the known values into the skidding distance equation:
d = v0 * t + (1/2) * a * t^2
= 14.0 * 5.60 + (1/2) * (-2.50) * (5.60)^2
= 78.4 - 78.4
= 0
Therefore, the skidding distance is 0 meters.
It's worth noting that this result indicates that the cyclist did not skid but rather came to a controlled stop without any skidding.
alex/jason I am not going to do them all for you.
All you need is
v = Vi + a t
x = Xi + Vi t + (1/2) a t^2