At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of i = (3.00 i − 2.00 j) m/s and is at the origin. At t = 2.00 s, the particle's velocity is = (6.60 i + 7.00 j) m/s. (Round your coefficients to two decimal places.)

(a) Find the acceleration of the particle at any time t. (Use the following as necessary: t.)
a = m/s2

(b) Find its coordinates at any time t. (Use the following as necessary: t.)
x = m
y = m

To find the acceleration of the particle at any time, we can use the formula:

a = (v - u) / t

where "a" is the acceleration, "v" is the final velocity, "u" is the initial velocity, and "t" is the time interval.

In this case, we are given the initial velocity u = (3.00 i - 2.00 j) m/s, the final velocity v = (6.60 i + 7.00 j) m/s, and the time interval t = 2.00 s.

Now, let's substitute these values into the formula to find the acceleration:

a = ((6.60 i + 7.00 j) - (3.00 i - 2.00 j)) / 2.00

Simplifying the equation, we get:

a = (6.60 i + 7.00 j - 3.00 i + 2.00 j) / 2.00

Combining like terms, we have:

a = (3.60 i + 9.00 j) / 2.00

To express the answer in the desired format, we round the coefficients to two decimal places, giving us:

a = 1.80 i + 4.50 j

Therefore, the acceleration of the particle at any time t is a = 1.80 i + 4.50 j m/s².

To find the coordinates of the particle at any time, we can use the equations of motion.

The equations of motion in the x and y directions are given by:

x = ut + (1/2)at²
y = vt - (1/2)at²

where "x" and "y" are the coordinates, "u" is the initial velocity, "v" is the final velocity, "a" is the acceleration, and "t" is the time.

In this case, we are given the initial velocity u = (3.00 i - 2.00 j) m/s, the final velocity v = (6.60 i + 7.00 j) m/s, and the acceleration a = 1.80 i + 4.50 j m/s². We also need to find the coordinates x and y at any time t.

Now, let's substitute these values into the equations of motion to find the coordinates:

x = (3.00 i - 2.00 j)t + (1/2)(1.80 i + 4.50 j)t²
y = (6.60 i + 7.00 j)t - (1/2)(1.80 i + 4.50 j)t²

Simplifying the equations, we get:

x = (3.00t + 0.90t²)i + (-2.00t + 2.25t²)j
y = (6.60t - 0.90t²)i + (7.00t - 2.25t²)j

Therefore, the coordinates of the particle at any time t are:
x = (3.00t + 0.90t²) m
y = (6.60t - 0.90t²) m