How Do You Calculate Velocity from a Position-Time Equation?

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Homework Help Overview

The problem involves calculating the velocity of an object moving along the x-axis, described by a position-time equation. The equation provided is x = a + b(t^2), where specific values for a and b are given.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of differential calculus to find velocity by differentiating the position equation with respect to time. There are questions about the differentiation process and how to apply it to find the velocity at a specific time.

Discussion Status

The discussion is focused on the differentiation of the position equation to derive the velocity function. Participants are actively engaging with the differentiation process and seeking clarification on the next steps after obtaining the derivative.

Contextual Notes

There is an implicit assumption that participants are familiar with basic calculus concepts, particularly differentiation. The specific values of a and b are provided, but the discussion does not clarify how these values influence the differentiation process.

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The position of an object moving along x-axis is given by x=a+b(t*t) where a =8.5m, b=2.5m/(s*s) and t is time. What is the velocity at t=2s? I think differential calculus should be used :confused:
 
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If that x equation is x = a+bt^2, then just differentiate wrt to time to get velocity.
 
Yupp, just get dx/dt and then make t = 2.
 
Is it this:
dx/dt = d(a+bt^2)/dt
After this what should I do?
 
Do you know how to differentiate?

If [itex]y = a + bx^2[/itex], what is dy/dx?

You have [itex]x = a + bt^2[/itex], and you know v=dx/dt, so what is v(t)?
 

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