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Particle x moves along the positive x-axis so that it's position at time t is less than equal to 0 is given by x(t)= 5t^3 - 9t^2 + 7. Is particle x moving toward the right at time t=1?

Respuesta :

So, at [tex]t=\frac{6}{5}[/tex], the velocity changes towards the right.

Velocity:

  • Velocity is the prime indicator of the position as well as the rapidity of the object.
  • It can be defined as the distance covered by an object in a unit of time.
  • Velocity can be defined as the displacement of an object in a unit of time.

Given that,

[tex]x(t)=5t^{3} -9t^{2} +7[/tex]

[tex]{x}'\left ( t \right )=15t^{2}-18t \\ {x}'\left ( 1 \right )=15t-18 \\ =-3 < 0[/tex]

Therefore, the particle is moving towards the left.

[tex]{x}'\left ( t \right )=0 \\ t=0 \\ t=\frac{18}{15}=\frac{6}{5}[/tex]

Learn more about the topic of Velocity: https://brainly.com/question/26417650

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