Calculating Distance for Negative Acceleration

In summary, the object with a negative acceleration will eventually reach a velocity of zero. To find the distance it travels until then, you can use the equation s = -u2/2a, where u is the initial velocity and a is the acceleration. However, if this equation is not yielding the correct distance, you can also use equation 1 (v = u + at) to solve for t when v = 0 and then plug that value into equation 3 (s = ut + 0.5 at^2).
  • #1
CarlosMarti12
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Homework Statement



Suppose an object has a velocity [itex]v[/itex] and an acceleration of [itex]a[/itex], where [itex]a[/itex] is negative. The object will eventually reach a velocity of zero [itex]v = 0[/itex]. How much distance will the object travel until [itex]v = 0[/itex]?

Homework Equations



v = u + at
s = 0.5(u+v)t
s = ut + 0.5 at2
v2 - u2 = 2as

The Attempt at a Solution



Since v2 - u2 = 2as, s = -u2/2a. I implemented this formula into a program I am using, but the object did not stop at the given distance. Am I doing something obviously wrong here? Any help would be greatly appreciated.
 
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  • #2


Well, using equation 1, set v = 0 and solve for t. Then plug that value into equation 3.
 

1. What is negative acceleration?

Negative acceleration, also known as deceleration, is the rate at which an object's velocity decreases over time. It is denoted by a negative value and can be caused by forces such as friction or air resistance.

2. How is distance calculated for negative acceleration?

To calculate distance for negative acceleration, you can use the equation d = v0t + (1/2)a0t2, where d is the distance, v0 is the initial velocity, a0 is the acceleration, and t is the time. This equation is derived from the area under the velocity-time graph.

3. How is negative acceleration represented on a velocity-time graph?

Negative acceleration is represented by a decreasing slope on a velocity-time graph. This means that the velocity is decreasing over time, resulting in a lower final velocity compared to the initial velocity.

4. Can negative acceleration result in a negative distance?

No, negative acceleration does not necessarily result in a negative distance. The distance is a scalar quantity and is always positive. However, the displacement, which takes into account the direction of motion, can be negative if the object is moving in the opposite direction of its initial velocity.

5. How does negative acceleration affect an object's motion?

Negative acceleration causes an object to slow down or decelerate. This means that the object's final velocity will be lower than its initial velocity, and it will take longer for the object to reach its final position. In some cases, negative acceleration can also cause an object to change direction, depending on the initial velocity and the magnitude of the acceleration.

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