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Verdich [7]
2 years ago
15

2. A car accelerates uniformly from +10.0 m/s to +50.0 m/s over a distance of 225 m. How long did it take to go that distance? S

how all your work, including the equation used, given and unknown quantities, and any algebra required. Make sure your answer has the correct number of significant figures.
Physics
1 answer:
artcher [175]2 years ago
7 0
Let's call the constant acceleration a.
At a time t, its speed will thus be v(t)=a*t+v0 where v0 is its initial speed, here 10 m/s. Hence v(t)=a*t+10.

From there we can deduce the position P(t)=a*t^2/2+10t+p0 where p0 is the initial position, here 0.

Hence P(t)=a*t^2/2+10t

Let's call T the time at which it's at 50 m/s, we know that P(T)=225m and that v(T)=50 m/s hence a*T+10=50 thus a=40/T and P(T)=(40/2+10)T=30T

Hence T=225/30=7.5

It took 7.5 seconds


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Correct response;

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<h3>Method by which the above option is selected</h3>

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Speed at the top of the circle, v = 20 m/s

Required:

The maximum radius of the circular path the roller coaster car.

Solution:

\displaystyle Centrifugal \ force, \, F_{c} = \mathbf{\frac{m \cdot v^2}{r}}

Where;

r = The radius of the circular path.

Weight of the roller coaster car = m·g = The centripetal force

Where;

g = Acceleration due to gravity = 9.81 m/s²

At equilibrium, we have;

Centrifugal force = Centripetal force

\displaystyle \frac{m \cdot v^2}{r}  = \mathbf{ m \cdot g}

Therefore;

\displaystyle r = \mathbf{ \frac{v^2}{g}}

Which gives;

\displaystyle r = \frac{20^2}{9.81} \approx 40.77

The maximum radius for safety of a roller coaster, r ≈ 40.77 meters

\displaystyle Range \ of \ radius \ of \ the \ circle = \frac{40.77}{4}  \leq Radius \ of \ circle \leq 40.77

Which gives;

Range of the radius of the circle = 10.2 ≤ Radius of circle ≤ 40.77

The correct option for safety considerations is therefore;

  • <u>C) 20 m</u>

<em>The possible question options are;</em>

<em>A) 5 m  B) 10 m  C) 20 m  D) 40 m  E) 80 m</em>

Learn more about centripetal force here:

brainly.com/question/12674230

7 0
2 years ago
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abruzzese [7]

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