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Lizwi
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How do you derive the results, a=dv/da
The equation a=dv/da is known as the derivative, which is a mathematical operation used to find the rate of change of a quantity with respect to another quantity. In this case, acceleration is the rate of change of velocity with respect to displacement.
The derivative allows us to find the instantaneous rate of change of a quantity, rather than the average rate of change over a period of time. This is important in understanding the behavior of objects in motion, as it gives us a more precise measurement of acceleration.
Sure, let's say an object is moving with a velocity of 10 m/s and its displacement is changing at a rate of 5 m/s. To find the acceleration, we would use the equation a=dv/da, where dv is the change in velocity and da is the change in displacement. Plugging in the values, we get a = 10/5 = 2 m/s^2.
The units of acceleration when using the derivative are typically meters per second squared (m/s^2). This is because we are finding the rate of change of velocity (m/s) with respect to displacement (m).
Yes, there are other ways to calculate acceleration, such as using the equations a=(vf-vi)/t (where vf is final velocity, vi is initial velocity, and t is time) or a=Δv/Δt (where Δv is the change in velocity and Δt is the change in time). However, the derivative is often used in more complex situations where the acceleration is changing continuously over time.