To find the acceleration, we first need to find the derivative of the velocity function with respect to time (t). However, we don't have v as a function of time, but as a function of displacement (x).

So, we need to use the chain rule for differentiation which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Given the velocity function v = 3x^2 - 2x, the derivative of v with respect to x (dv/dx) is 6x - 2.

Now, we know that acceleration a = dv/dt. But we have dv/dx. So, we can write a = dv/dt = dv/dx * dx/dt.

But dx/dt is just the velocity v. So, we have a = (dv/dx) * v.

Substituting the given values, we get a = (6*2 - 2) * (3*2^2 - 2*2) = 8 * (12 - 4) = 8 * 8 = 64 m/s^2.

So, the acceleration at x = 2m is 64 m/s^2.

Question

To find the acceleration, we first need to find the derivative of the velocity function with respect to time (t). However, we don't have v as a function of time, but as a function of displacement (x).

So, we need to use the chain rule for differentiation which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Given the velocity function v = 3x^2 - 2x, the derivative of v with respect to x (dv/dx) is 6x - 2.

Now, we know that acceleration a = dv/dt. But we have dv/dx. So, we can write a = dv/dt = dv/dx * dx/dt.

But dx/dt is just the velocity v. So, we have a = (dv/dx) * v.

Substituting the given values, we get a = (6*2 - 2) * (3*2^2 - 2*2) = 8 * (12 - 4) = 8 * 8 = 64 m/s^2.

So, the acceleration at x = 2m is 64 m/s^2.

Knowee AI · Accepted Answer

To find the acceleration, we first need to find the derivative of the velocity function with respect to time (t). However, we don't have v as a function of time, but as a function of displacement (x).

So, we need to use the chain rule for differentiation which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Given the velocity function v = 3x^2 - 2x, the derivative of v with respect to x (dv/dx) is 6x - 2.

Now, we know that acceleration a = dv/dt. But we have dv/dx. So, we can write a = dv/dt = dv/dx * dx/dt.

But dx/dt is just the velocity v. So, we have a = (dv/dx) * v.

Substituting the given values, we get a = (6*2 - 2) * (3*2^2 - 2*2) = 8 * (12 - 4) = 8 * 8 = 64 m/s^2.

So, the acceleration at x = 2m is 64 m/s^2.

For motion of an object along the x-axis the velocity v depends on the displacement x as v = 3x2 – 2x, then what is the acceleration at x = 2m.

Question

For motion of an object along the x-axis the velocity v depends on the displacement x as

Solution

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