Finding the magnitude of acceleration

In summary, a toy train is released at 1.42 m with a speed of 1.86 m/s and rolls at a steady speed for 2.04 s before one wheel begins to stick. The train comes to a stop at 5.06 m from the point of release. To find the magnitude of the train's acceleration after the wheel begins to stick, you can calculate the distance traveled during the constant velocity time and subtract it from the total distance traveled. Then, using the known values of distance, initial velocity, and final velocity, you can solve for acceleration using a kinematic equation.
  • #1
mcryder16
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Homework Statement



A toy train is pushed forward and released at x0=1.42 m with a speed of 1.86 m/s. It rolls at a steady speed for 2.04 s, then one wheel begins to stick. The train comes to a stop 5.06 m from the point at which it was released. What is the magnitude of the train’s acceleration after its wheel begins to stick?

Homework Equations



I can't figure out the equation or how to start this problem?

The Attempt at a Solution

 
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  • #2
Draw a picture, and remember that when the toy is released the toy has constant velocity until its wheel gets stuck. So calculate the distance traveled in that time.

Once you have that you can subtract all the distances to get the distance traveled when under a negative acceleration due to the sticky wheel. You will have distance travelled, initial velocity, and final velocity. Then you can solve for the 'a' using a well-chosen kinematic equation.
 
  • #3


To find the magnitude of acceleration, we can use the equation a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. In this case, we know that the initial velocity (vi) is 1.86 m/s and the final velocity (vf) is 0 m/s (since the train comes to a stop). We also know that the time (t) is 2.04 s. So, the equation becomes:

a = (0 m/s - 1.86 m/s)/2.04 s = -0.91 m/s^2

This means that the magnitude of the train's acceleration after its wheel begins to stick is 0.91 m/s^2. This negative sign indicates that the train is decelerating.
 

1. What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude (how much) and direction.

2. How do you find the magnitude of acceleration?

The magnitude of acceleration can be calculated by dividing the change in velocity by the change in time. The formula is: magnitude of acceleration = (final velocity - initial velocity) / time.

3. What units are used to measure acceleration?

Acceleration is typically measured in meters per second squared (m/s^2) in the metric system and feet per second squared (ft/s^2) in the imperial system.

4. How does acceleration affect an object's motion?

Acceleration can cause an object to change its speed, direction, or both. If an object has a positive acceleration, it is speeding up. If it has a negative acceleration, it is slowing down. A constant acceleration will result in a linear change in velocity over time.

5. How is acceleration related to Newton's Second Law of Motion?

Newton's Second Law states that the force acting on an object is equal to its mass multiplied by its acceleration (F=ma). This means that the greater the acceleration of an object, the greater the force acting on it. In other words, a larger force is needed to accelerate an object with a higher mass compared to one with a lower mass.

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