Motion of a particle and zero velocity

[Alexanddros81]

Homework Statement

11.7 The motion of a particle is defined by the relation ##x = 2t^3 - 15t^2 + 24t + 4
where x is expressedin meters and t in seconds. Determine (a) when the velocity zero ,
(b) the position and the total distance traveled when the acceleration is zero

Homework Equations

The Attempt at a Solution

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Can you check if my solution is correct?

 

[tnich]

Homework Statement

11.7 The motion of a particle is defined by the relation ##x = 2t^3 - 15t^2 + 24t + 4
where x is expressedin meters and t in seconds. Determine (a) when the velocity zero ,
(b) the position and the total distance traveled when the acceleration is zero

Homework Equations

The Attempt at a Solution

View attachment 222710
[/B]
Can you check if my solution is correct?

First, let me comment that your printing is neat and readable in the image. However, you are much more likely to get responses to your questions if you type in your solution. Many helpers will not respond otherwise.

That said, yes, your solution looks correct.

 

[PeroK]

Looks good to me.

 

[Alexanddros81]

Is my last sentence correct?

I think it should be $x(2.5) - x(1) = 1.5 - 15 = -13.5$ (moving in opposite direction).
Overall though the particle travels a total distance of 11+13.5 = 24.5