How do you isolate the t-variable in the acceleration formula

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To isolate delta-t in the acceleration formula, the integration method can be applied, leading to the equation ∫(1/a) dv = ∫ dt + C. If distance traveled is known and acceleration is constant, the equation v_0Δt + (1/2)ΔvΔt = d can be used to find delta-t. This relationship is visually represented in a velocity-time graph, where the area under the curve corresponds to distance. Understanding these methods allows for effective calculation of time in motion equations. The discussion emphasizes the importance of integration and graphical interpretation in isolating variables in kinematic equations.
wScott
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acceleration = delta-v / delta-t

How do I isolate delta-t?
 
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via integration

\int \frac{1}{a}dv = \int dt \ + \ C
 
Last edited:
delta v / acceleration = delta t
 
wScott said:
acceleration = delta-v / delta-t

How do I isolate delta-t?
If you are given the distance travelled, as I suspect is the case, and if there is constant acceleration, use:

v_0\Delta t + \frac{1}{2}\Delta v\Delta t = d

This is easy to see using a v-t graph (in which the area under the graph is the distance).

AM
 

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