Have you ever ridden on a rollercoaster and felt your heart drop as you were going downhill? Have you asked yourself how getting these feelings were possible? The answer is math. You may ask what math has to do with rollercoasters. Math is the reason for everything and anything that has to do with rollercoasters. Without math‚ it would be impossible to even be able to create one. To build a rollercoaster you need to be able to use numbers when talking about the costs‚ taking measurements‚ calculating
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Team Control Number For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ 31285 Problem Chosen A For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ 2014 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to your solution paper.) Type a summary of your results on this page. Do not include the name of your school‚ advisor‚ or team members on this page
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just need to find the time. We find the time‚ by applying the average velocity formula to both parts of the journey‚ and solving for time. Δt1 = Δx1/ Vavg ‚ 1 = 30/60 = 0.5 hours Δt2 = Δx2/ Vavg ‚ 2 = 30/30 = 1.0 hours Vavg = Δx/Δt = (30 + 30) / (0.5 + 1.0) Vavg = 40 mi/hr Questions 2 – 4 relate to two particles that start at x = 0 at t = 0 and move in one dimension independently of one another. Graphs‚ of the velocity of each particle versus time are shown below Particle A Particle B
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Write ib unit. velocity’ bi I)t"* velocity-time graPh‚ when an obiect has (i) unifortdy accelerated (ii) uniformly retarded velocity. fror" that if u Uoayi" thrown ve*ically upwatd‚ the time of ascent is equal to the time ffi of descent. Th;;r*h .ttracts the moon. Does the moon also attract the earth ? If it does‚ why does ttre earth not move towards the moon ? 6) A bullet of mass 1‚0 g is fired with a velocity of 400 m/s from a gun of mass 4 kg’ What is ‚‚xldge recoil velocity of the gun
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line along a road. It’s distance x from a stop sign is given as a function of time t by the equation‚ where and. Calculate the velocity of the car for each of the time given: (a) t = 2.00s; (b) t = 4.00s; (c) What will be the time when the acceleration is equal to zero? Solution: By getting the derivative of the distance as a function of time we can get the velocity as a function of time. Substitute the values of α and β a) Given t = 2.00s b)
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Equations of Motion Worksheet 1. A car moving at a velocity of 25 m/s‚ accelerates at a rate of 6 m/s2. Find its velocity after 3s. 2. An object is dropped from rest. Calculate its velocity after 2.5s if it is dropped: a. On Earth‚ where the acceleration due to gravity is 9.8m/s2. b. On Mars‚ where the acceleration due to gravity is 3.8m/s2. 3. A motorbike is travelling with a velocity of 3m/s. It accelerates at a rate of 9.3m/s for 1.8s. Calculate the distance it travels in this time. 4. A Tesla
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r a c t The three-dimensional flow field and the flow pathlines within a Tesla disc turbine have been investigated analytically and computationally. The description of the flow field includes the three-dimensional variation of the radial velocity‚ tangential velocity and pressure of the fluid in the flow passages within the rotating discs. A detailed comparison between the results obtained from the analytical theory and computational fluid dynamic (CFD) solutions of Navier–Stokes equations is presented
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meters 10 meters 2 meters 8. A bicyclist going south at 5 m/s passes a bicyclist going north at 5 m/s‚ they have the same? (2.09-2.11) 9. Define acceleration‚ speed‚ velocity‚ distance and displacement. (2.01‚ 2.16‚ 2.19) 10. The slope of a Velocity versus Time graph will tell you the object’s what (2.23) 11. On a velocity versus time graph the quantity the area between the graph line and the x-axis represents the change in ________________________ of the object. Refer to image below for
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a rotating turntable. The different vectors representing velocity for the travelling marble are shown below. Notice that the size of the vector remains the same but the direction is constantly changing. Because the direction is changing‚ there is a ∆v and ∆v = vf - vi ‚ and since velocity is changing‚ circular motion must also be accelerated motion. vi ∆v vf -vi vf2 If the ∆t in-between initial velocity and final velocity is small‚ the direction of ∆v is nearly radial (i.e. directed
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acceleration of -1.5m/s2. What is the final velocity of the car? How far does the car travel in this time interval? vf = vi + a(Dt) or vf = (0 m/s) + (-1.5 m/s2)(5.0 s) = -7.5 m/s Dx = vi(Dt) + 1/2a(Dt)2= Dx = (0)(5.0 s) + 1/2(-1.5 m/s2)(5.0 s)2 = -18.75 m or -19 m (sig figs). 2E 1. Find the velocity after the stroller has traveled 6.32 m. (A person pushing a stroller starts from rest‚ uniformly accelerating at a rate of 0.500m/s2. What is the velocity of the stroller after it has traveled 4.75m
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