I still need help on my other question as well...
A runner hopes to complete the 10,000 m run in less than 30.0 min. AFter running at constant speed exactly 27.0 min there are still 1100 m to go. The runner must then accelerate at .20 s^-2 m for how many seconds in order to achieve the desired time?
ok well I foudn if you consider the first part of the run to have zero acceleration then you get 5.494 s^-1 m for the initial velocity for the second part of the race before the acceleration occurs...
so I'm trying to solve for t for the second part
reorginizing this equation
X = Xo + Vo t + 2^-1 a t^2
has more than one t in it and can't be taken out because there is a Vo and a acceleration
my only other choice is
a = t^-1 (V - Vo)
the final velocity can be assumed to be zero which it wouldn't be because most people would continue to run after the finish line but even if you did assume it to be zero then when you rearanged for time
t = a^-1 - Vo
I get a negative time...
thanks for help on other question =]
Is the answer to (c) correct by the way for the other problem I didn't know how fast it would be accelerating realtive to the larger block because the larger block would be accelerating more at 5.2 s^-1 m and the smaller block accelerates at 3.2 s^-1 m so I wasn't sure how much the smaller block is accelerating with reference to the larger block
An arrow is fired with a speed of 24.0 m/s at a block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. During this process the arrow's deceleration has a magnitude of 1750 m/s2 and the block's acceleration has a magnitude of 450 m/s2
To find the time needed to achieve the desired finish time, let's break down the problem step by step.
1. First, let's calculate the initial velocity (Vo) for the second part of the race before acceleration occurs.
We know that the runner ran for exactly 27.0 minutes (1620 seconds) and covered 1100 meters. Since the runner is running at a constant speed during this time, we can calculate the initial velocity (Vo) using the formula:
Vo = X / t
Vo = 1100 / 1620
Vo ≈ 0.679 s^-1 m (approximately)
2. Next, let's find the acceleration (a) that the runner needs to achieve in order to complete the remaining distance in the desired time.
We are given the acceleration value of 0.20 s^-2 m.
3. Now, we can calculate the time it takes to achieve the desired time by using the formula:
t = (a - Vo) / a
t = (0.20 - 0.679) / 0.20
t ≈ -2.395 s (approximately)
It appears that the result is a negative time, which doesn't make sense. This may imply that the initial assumptions or calculations are incorrect. To clarify, recheck your initial calculations for the initial velocity (Vo) and ensure that all units are consistent.