Particle in Motion | Position at t = 2.70 s and t = 2.70 s + Δt | x = 6t^2

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To find the position of a particle at t = 2.70 s, the equation x = 6t^2 is used, resulting in x = 6(2.70)^2. For part b, the position at t = 2.70 s + Δt requires calculating the change in position, represented as dx = 12tΔt. The final position is then expressed as xf = x + dx, incorporating the initial position and the change due to Δt. This approach allows for understanding the particle's motion over a small time increment.
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Homework Statement


The position of a particle moving along the x-axis varies in time according to the expression
x = 6t^2, where x is in meters and t is in seconds. Evaluate its position at the following times.
(a) t = 2.70 s

(b) t = 2.70 s + Δt
xf =

Homework Equations


(Use Deltat for Δt.)


The Attempt at a Solution


I understand that for part A, all i do is plug in (2.70) into 6(2.70)^2 to get the answer.
But what do i do for part b with that "Δt"?? and the answer for part b is supposed to be in symbolic format
 
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dx = 12*t*dt
And xf = x + dx.
 
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