The Fastest (and Most Expensive) Car! The table shows test data f...

Question

The Fastest (and Most Expensive) Car! The table shows test data for the Bugatti Veyron Super Sport, the fastest street car made. <TABLE> The car is moving in a straight line (the x-axis). (a) Sketch a vx–t graph of this car’s velocity (in mi/h) as a function of time. Is its acceleration constant? (b) Calculate the car’s average acceleration (in m/s2) between (i) 0 and 2.1 s; (ii) 2.1 s and 20.0 s; (iii) 20.0 s and 53 s. Are these results consistent with your graph in part (a)? (Before you decide to buy this car, it might be helpful to know that only 300 will be built, it runs out of gas in 12 minutes at top speed, and it costs more than $1.5 million!)

Accepted Answer

Hey everybody. So today we're dealing with the problem about acceleration and time. So we're being told that an engineer has made a very fast toy truck and has values for velocity for this time. And we're being asked to determine whether the acceleration is constant by using a graph or a sketch of a velocity versus time graph and what the average acceleration of the toys at time between zero and 1.5 seconds, 1.5 and 12 seconds and 12 and 25 seconds. So let's tackle the first part of this problem 1st and I've gone ahead and I've plotted out our values below once again. Now to draw this as a graph, what I want to do first and let's just move this up a little bit, I'd like to convert our miles per hours and two m/s, not only for the sake of drawing the graph, but it'll also help us later on as we do our um calculations for acceleration soon. So make another column right here. We can convert MPH to kilometers or sorry meters per second using some conversion factors. So recall that one mile is equal to six or sorry, 1.609609 kilometers, one km is equal to 1000 m And one hour is equal to 3600 seconds. So if we convert 33.5 mph to meters per second, well, I would go 30 and let's write this out down here. If you convert it, we go 33.5 mph. So the first thing we wanna do is convert our kilometers to our our miles to kilometers. Just 1.609 km per mile four mi will cancel out. Then we want to convert our kilometers two m so we have m per kilometer scenario, kilometers will cancel out and then we can convert hours to seconds to have 30 600 troops. We have Excuse me, we have one hour for every 3600 seconds because we need seconds in the denominator. So our hours will cancel out and summing this up. We get a value of 15.0 m per second, so we can reuse that same set of conversions for each of the other values and we get our velocity in meters per second As will be zero here, it will be 15.0 m/s. I rewrote the units up there my bad. We have 77.8 And finally 84.0 meters per second. And I'm just going to. So from here we can go ahead and sort of draw out our graph. We can draw out the graph of what we have. So let's just make a sort of rudimentary graph here where the have the y axis and the X axis right here. Now this is velocity versus time graphs. So the X access is going to be velocity in meters per second. Or sorry, the y axis is going to be velocity meters per second and the X axis is going to be time in seconds. This is the origin. 0, 0. Let's just plot this out at five seconds. 10 oops, 20 25 seconds. And let's sort of go by tens in the extra it's 10 2030 40 60 70 80 90. Just write that out. Getting your values here 30, 20 and 10. So all that in mind. Let's go ahead and plot our values. So we have a first point at We have the next add 1.5 and 15 so it'll fall somewhere around here. Let's say Our next sits at 1277.8. So 12 will be about here, 77.8 will be close to 80. So we'll say just about right here. And then the next one is at 25 and 84 all the way here, about midway between 80 and 90. So for it to draw this out, connect the dots, so to speak right? So as you can see the acceleration here, because remember, acceleration is equal to slope on a V versus T graph. Change in v over change in t the slope here, if we wanted it to be constant, would mean we would need a straight line on our velocity versus time graph because then the slope will be the same at all points and acceleration will be constant, not zero, but constant throughout. Since we don't have a straight line, we have curves and ridges and whatnot acceleration, acceleration is not constant. So going back to our answer choices, we can rule out answer choices A and B simply because acceleration or oops, sorry, we can rule out answers to C and D because acceleration is definitely not constant, which means these two clauses are invalid. So going back down, we can go ahead and start answering the second part of this question which is asking us to find the accelerate the average acceleration between different points in time. And we can use this because remember we just wrote out our slope and acceleration is the slope of a V versus T graph, which means we just need to find the change of velocity over the different changes in time periods. So let's start with the first Time period which will write as a V one Where this time period is one. This time period is two And this time period is three. Okay, so this happens between Uh time zero and 1.5. So writing it out, we get 15 Over 1.5 minus zero. What she calls 15/ 0.5 or 10 m per second squared, We can do the same for the second time period is delta v over delta T over delta T. Now between 12 and 1.5 seconds and 77.8 and 15 m/s. So comes 77. minus 15, divided by 12 -1.5, Which gives us 62.8 meters per second over 10.5 seconds. Right? And that'll give us 5.98 m per second squared. Finally, for the third time period we can do the same thing. We're now dealing with 84 m/s at 25 seconds. So between here, Oops, so this would be one. Oops. This time period one. This is time period too. This is time period three. So adding that up, we get 84 -77.8 over 25 -12, which gives us 10. Oops. Ah last time I calculated here real quick just to double check, gives us 6.2 m/s over seconds, which gives us 0. meters per second squared. So with that in mind we go back and look at her answer choices and I apologize, this is incorrect. This should say 0.469 or 476. My Ben 76 m/s squared. But an answer choice will be a I hope this helps. And I look forward to seeing you all In the next one