With an average acceleration of −2.2 m/s^2,
how long will it take a cyclist to bring a bicycle
with an initial speed of 14.5 m/s to a complete
stop?
Answer in units of s.
v = Vi + a t
0 = 14.5 - 2.2 t
t = 14.5/2.2
t = 6.59 s
next get the distance
x = Xi + Vi t + (1/2) a t^2
x = 0 + 14.5(6.59) - 1.1(6.59)^2
= 95.6 - 47.8 = 47.8 meters
wow, half a football field !
Well, let's see. The cyclist has an average acceleration of -2.2 m/s^2 and wants to bring the bicycle to a complete stop. So it's like they're on a downhill road going uphill! That's quite a challenge!
To find out how long it will take, we can use the equation:
Vf = Vi + at
Where Vf is the final velocity (in this case, 0 m/s since we want to stop completely), Vi is the initial velocity (14.5 m/s), a is the acceleration (-2.2 m/s^2), and t is time (what we're looking for).
Plugging in the numbers:
0 = 14.5 - 2.2t
Now, let's solve for t:
2.2t = 14.5
t = 14.5 / 2.2
t ≈ 6.59 seconds
So, it will take the cyclist approximately 6.59 seconds to bring the bicycle to a complete stop. Just enough time for them to ponder the mysteries of life and wonder why they decided to bike on an uphill road in the first place!
To find the time it will take for the cyclist to bring the bicycle to a complete stop, we can use the equation:
v = u + at
where:
v = final velocity (0 m/s, since the bicycle comes to a complete stop)
u = initial velocity (14.5 m/s)
a = acceleration (-2.2 m/s^2)
t = time
Rearranging the equation to solve for time (t), we have:
t = (v - u) / a
Plugging in the values, we get:
t = (0 - 14.5) / (-2.2)
Simplifying the expression, we have:
t = -14.5 / -2.2
t ≈ 6.6 s
Therefore, it will take approximately 6.6 seconds for the cyclist to bring the bicycle to a complete stop.
To find the time it takes for the cyclist to bring the bicycle to a complete stop, we can use the kinematic equation:
vf = vi + at
Where:
- vf is the final velocity (which is 0 m/s, as the bicycle comes to a complete stop)
- vi is the initial velocity of 14.5 m/s
- a is the acceleration of -2.2 m/s^2
- t is the unknown time we're trying to find
Rearranging the equation to solve for time (t), we get:
t = (vf - vi) / a
Substituting the given values:
t = (0 m/s - 14.5 m/s) / -2.2 m/s^2
Simplifying the equation, we get:
t = -14.5 m/s / -2.2 m/s^2
Notice that the negative signs will cancel out, resulting in a positive value for time. Negative acceleration is just indicating a decrease in velocity.
t = 14.5 m/s / 2.2 m/s^2
Calculating this division, we find:
t ≈ 6.59 seconds
Therefore, it will take the cyclist approximately 6.59 seconds to bring the bicycle to a complete stop.