Rocket-powered sleds are used to test the responses of humans to acceleration. Starting from rest, one sled can reach a speed of 444 m/s in 1.80 s and can be brought to a stop again in 2.15 s.
(b) Find the acceleration of the sled as it is braking and compare it to the magnitude of the acceleration due to gravity.
2Your answer is incorrect.g
a = (V2-V1)/t = (0 -444)/2.15
= - 207 m/s^2
207/9.8 = 21 times magnitude of gravity
Well, if my calculations are correct (and let's be honest, they usually aren't), the acceleration of the sled during braking can be found using the formula:
acceleration = (final velocity - initial velocity) / time
In this case, the final velocity is 0 m/s (since the sled comes to a stop), the initial velocity is 444 m/s, and the time is 2.15 seconds (because I said so).
So, plugging in the values:
acceleration = (0 m/s - 444 m/s) / 2.15 s
Simplifying that, we get:
acceleration = -206.05 m/s^2
Now, let's compare this acceleration to the magnitude of the acceleration due to gravity, which is approximately 9.8 m/s^2 (or larger if you live on a planet with a fast roller coaster).
So, it seems like the acceleration of the sled during braking is a bit more intense than the good ol' acceleration due to gravity. Time to buckle up and hold on tight!
To find the deceleration (acceleration while braking) of the sled, we need to use the equation:
Acceleration = change in velocity / time
The change in velocity can be calculated as follows:
Change in velocity = final velocity - initial velocity
= 0 - 444 m/s (since it comes to a stop)
= -444 m/s
The time taken to come to a stop is 2.15 s. Therefore, we can calculate the acceleration as:
Acceleration = (-444 m/s) / (2.15 s)
≈ -206.05 m/s^2
The negative sign indicates deceleration or braking.
To compare the acceleration to the magnitude of acceleration due to gravity, we need to know the value of acceleration due to gravity. On the surface of the Earth, the average value of acceleration due to gravity is approximately 9.8 m/s^2.
Comparing the magnitude of the sled's deceleration (-206.05 m/s^2) to the acceleration due to gravity (9.8 m/s^2), we find that the sled's deceleration is much greater than the magnitude of the acceleration due to gravity.
To find the acceleration of the sled as it is braking, we need to use the equation of motion:
v = u + at
where:
v = final velocity (0 m/s, since the sled comes to a stop)
u = initial velocity (444 m/s)
a = acceleration
t = time (2.15 s)
Rearranging the equation, we have:
a = (v - u) / t
Substituting the given values, we get:
a = (0 m/s - 444 m/s) / 2.15 s
a = -444 m/s / 2.15 s
a = -206.05 m/s²
The negative sign indicates that the sled is experiencing a deceleration.
Now, let's compare this acceleration to the magnitude of the acceleration due to gravity (g). The acceleration due to gravity is typically around 9.8 m/s².
Since the sled's braking acceleration is -206.05 m/s² and the acceleration due to gravity is 9.8 m/s², we can see that the sled's braking acceleration is much larger in magnitude than the acceleration due to gravity.
So, the acceleration of the sled as it is braking is much greater (in magnitude) than the acceleration due to gravity.