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

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To calculate velocity from the position-time equation x = a + b(t^2), where a = 8.5m and b = 2.5m/(s^2), one must differentiate the equation with respect to time. The derivative dx/dt yields the velocity function v(t). After differentiating, substituting t = 2s into the velocity function provides the specific velocity at that time. The discussion also briefly touches on differentiation concepts, indicating a broader interest in calculus applications. Understanding these principles is essential for solving similar physics problems effectively.
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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 y = a + bx^2, what is dy/dx?

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

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