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A motorcycle has a constant acceleration of 2.5 $\mathrm{m} / \mathrm{s}^{2} .$ Both the velocity and acceleration of the motorcycle point in the same direction. How much time is required for the motorcycle to change its speed from (a) 21 to $31 \mathrm{m} / \mathrm{s},$ and $\quad$ (b) 51 to 61 $\mathrm{m} / \mathrm{s} ?$

(a) $t=4 \mathrm{s}$(b) $t=4 \mathrm{s}$

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

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the acceleration of the motorcycle and this problem is 2.5 meters per second squared and were asked to find how long it takes to go from a velocity. An initial velocity of two point until 21 meters per second is our initial velocity, and the velocity to later time is 31 meters per second. So to find the time we can use the equation, B equals V not plus acceleration times time and if you look at it before we even plug numbers and we could subtract me not from those sex and we would just have the minus B not is equal to 80 which is really just a definition of acceleration. Acceleration is the change in velocity over time. If you multiply both sides of that by t, you get re the Delta V, which is B minus. We not is equal to a 10 50. So if I do it this way, um, the 31 minus 2 21 is on the left hand side and that's equal to 2.5 or 2.5 meters per second squared times. T so 31 minus 21 is just 10 equals 2.5 leaders per second squared times t. And then we divide both sides by 2.5, and we have a four second time interval. Now, if the numbers were different, the velocities were in the second part of the problem. It says, What? How long does it take to go from 51 to 61? Well, so our initial velocity in this case is 51 tells us, Rewrite it up here, Asare givens. And our final velocity is 61. And everything is positive in this problem because they said the acceleration and the velocity were in the same direction. So we don't need to worry about, um, positives, negatives. Everything could just be positive. So, um, for the second part of the problem, we're still going to do a 61 minus 51 which is exactly the same number we get. Always attract 31 21. So it doesn't matter what the velocities specifically are. So gonna get 10 over here. Um, all that matters is the change in velocity. So if the change in velocity is 10 our acceleration is still 2.5. Our time is still going to be four seconds. Z quantity

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