When is the particle speed up/slowing down

In summary, the position of a particle can be represented by the equation s=2t^2-9t^2 where t is in seconds and s is in meters. To determine when the particle is speeding up or slowing down, the first derivative (velocity) and second derivative (acceleration) can be calculated. When the velocity and acceleration have the same sign, the particle is speeding up, and when they have opposite signs, it is slowing down. This can be determined by finding the values of t for which the velocity and acceleration are positive or negative, which can only change at the zeros.
  • #1
betsinda
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Homework Statement



The postion of a particle is given by s=2t^2-9t^2 where t is in seconds and s in meters

a) when is the particle speeding up/slowing down

Homework Equations





The Attempt at a Solution



I have calculated the
1st derivative (velocity) as 6t^2-18t
2nd derivative (acceleration) as 12t-18

and I know that the particle is speeding up when the velocity and the acceleration have the same sign and slowing down when they have opposite signs. However I am not sure how to express this to answer the question.

Thanks
 
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  • #2
Find the values of t for which the velocity and for which the acceleration is positive/negative. Hint: They can only change sign at the zeros.
 

1. When does a particle speed up?

A particle speeds up when it experiences a net external force in the direction of its motion. This force can come from various sources such as gravity, electric or magnetic fields, or other objects colliding with the particle.

2. What causes a particle to slow down?

A particle slows down when it experiences a net external force in the opposite direction of its motion. This force can come from sources such as friction, air resistance, or an opposing force from another object.

3. Is there a maximum speed a particle can reach?

According to the theory of relativity, there is a maximum speed at which particles can travel, known as the speed of light. This speed is approximately 299,792,458 meters per second in a vacuum and cannot be exceeded by any particle.

4. How does the mass of a particle affect its speed?

In classical mechanics, the mass of a particle does not directly affect its speed. However, in relativistic mechanics, as the speed of a particle approaches the speed of light, its mass increases, making it more difficult to accelerate and reach higher speeds.

5. Can a particle change its speed without an external force?

No, according to Newton's first law of motion, an object at rest will stay at rest and an object in motion will stay in motion at a constant speed and direction unless acted upon by an external force. Therefore, a particle cannot change its speed without an external force acting on it.

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