Final answer:
The acceleration vector can be written in terms of unit tangent and unit normal vectors using the formula A(t) = a(t) = (at)x + (an)y, where at is the tangential acceleration and an is the normal acceleration. Given a specific acceleration vector, we can calculate the tangential and normal accelerations, and then express the acceleration vector in terms of the unit tangent and unit normal vectors by normalizing it.
Step-by-step explanation:
The acceleration vector can be written in terms of unit tangent and unit normal vectors as follows:
A(t) = a(t) = (at)x + (an)y
where at is the tangential acceleration and an is the normal acceleration.
Given that the acceleration vector: a(t) = 5.0i + 2.0j - 6.0km/s² at t = 2 s, we can determine the tangential and normal accelerations at t = 2 s. We can then write the acceleration vector in terms of the unit tangent and unit normal vectors.
The magnitude of the acceleration at t = 2 s is given by:
|a(2 s)| = √(5.0² + 2.0² + (-6.0)²)
To find the direction in unit vector notation, we can normalize the acceleration vector by dividing it by its magnitude:
a(2 s) = (√(5.0² + 2.0² + (-6.0)²))/(√(5.0² + 2.0² + (-6.0)²))