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A cart is driven by a large propeller or fan, which can accelerate or decelerate the cart. The cart starts out at the position $x=0 \mathrm{m}$ , with an initial velocity of $+5.0 \mathrm{m} / \mathrm{s}$ and a constant acceleration due to the fan. The direction to the right is positive. The cart reaches a maximumposition of $x=+12.5 \mathrm{m},$ where it begins to travel in the negative direction. Find the acceleration of the cart.
$a=-1 \mathrm{m} \cdot \mathrm{s}^{-2}$
Physics 101 Mechanics
Chapter 2
Kinematics in One Dimension
Motion Along a Straight Line
Cornell University
University of Washington
University of Sheffield
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were given that a cart starts at Position X equals zero and reaches of the loss or starts of the velocity of five meters per second in the positive direction and they just think that the acceleration is constant. We don't know what it is, but it's constant, which enables us to use our constant acceleration equations a day later point. It has reached a position of 12.5 meters, but at this point it says it begins to travel in the negative direction. So if that's the case, it must reach a speed of zero because it can't be going in the positive direction and then suddenly start moving in the negative direction without passing through a speed of zero. So the velocity at that moment in time would be zero meters per second. So we can use the equation. V is equal to be not squared, plus two times acceleration times The displacement where V is zero. We not is five the acceleration. We don't know what the displacement we dio. So if I move the five square to the left hand side of the equation, five squared is 25. So I have a negative 25 meters square per second squared is it to two times 12.5, also 25. So I can say 25 meters times A, which makes our math really easy. Will divide 25 negative 25 meters square per second, squared by 25 liters on both sides and we have an acceleration of negative one meters per second squared.
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