The planet hunters have already unwrapped some of their haul, using telescopes to closely study and even image a small number of unappetizingly uninhabitable gas-giant worlds. Swat any star hard enough with state-of-the-art instrumentation, it seems, and it will eventually spill out new worlds like candy pouring from a split piñata. In that time they and their colleagues have found thousands of exoplanets-planets orbiting stars other than our sun-and have statistically surmised that hundreds of billions more await discovery in our galaxy alone. Um, enough now is this for us to say that the instantaneous velocity as time, bro, just two seconds is negative 24 in this case, feet per second.You won’t hear them say it, but some of the world’s most acclaimed astronomers have been frustrated for the better part of two decades. It's so close to two that its prey, um school knows that as we get closer and closer to two with our time, the velocity keeps decreasing and decreasing it closer to negative 24. And we could knows that the closer and closer week que zero seconds, Uh, because instantaneous velocity will be you can view it as if we were to plug in 2.1 So many. So we notice here that 2.5, it's negative. Now to find the instantaneous philosophy, Um, we could do this graphically. 32 negative, 25.6, negative 24.8 and negative 24.16 And these represents the average velocities or the ball thrown in the air at 0.5 point 105 and 0.1 seconds after t equals two. For the displacement of why to solve for T. This would give us negative 16 negative 2.56 and negative 1.24 and the negative 0.24 So now, since we know that the is you go to the displacement of X over the displacement of two, we can just plug in our values for the displacement to you in our values. So we're gonna take the times we just came up with why and subtracting from 16. Why? We're just going Teoh, plug all of these values, Um, we're gonna subtract 16 from And the reason we're subtracting 16 from them is because from why is at equal to tease you would have to, um why equals 16 cause we're trying to find the displacement from AT T equals two vs at these four different time points. At that time, This will give us zero 13.44 14.76 and 15.7 six. And now we just plug in these four values of T into why? To get the distance. The third item is 0.5 seconds and this would give us to buy.
The next item, at 0.1 seconds will be 0.1. A team 0.5 seconds is going to be two points. So displacement of X is going to be represented is why in this problem, and we have the displacement of oy and then finally, we can use all of those to give us the velocity at a given point. Then we will get the value of why our X It's gonna be why, in this case, because, um, we're working with a ball that is in the air. We're just gonna make a little tape, so you will have the displacement of tea, each one we'll have what time that gives us looking. So to solve this problem for the four different time periods, we'll have to come up with the distances, threat and the different times there. So we know that the average velocity for any given time period is going to be equal to Displacement X over the displacement of teeth.
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