# An object's two dimensional velocity is given by #v(t) = ( 3t^2 - 2t , 1- 3t )#. What is the object's rate and direction of acceleration at #t=4 #?

The rate of acceleration is

The acceleration is the derivative of the velocity.

Therefore,

The rate of acceleration is

The direction is

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To find the acceleration, take the derivative of the velocity function with respect to time, then evaluate it at t=4. The acceleration vector is given by a(t) = (6t - 2, -3). So, at t=4, the acceleration vector is a(4) = (22, -3). The rate of acceleration is the magnitude of the acceleration vector, which is √(22^2 + (-3)^2) ≈ 22.44 units per second squared. The direction of acceleration is the direction of the acceleration vector, which is approximately 272.4 degrees counterclockwise from the positive x-axis.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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