Question

At t= 0, a particle starts from rest at x= 0, y = 0, and moves in the xy plane with an acceleration a⃗ = (4.0i^ + 3.0j^)m/s2. Assume t is in seconds.. . Determine the x component of velocity as a function of time t.. . etermine the ycomponent of velocity as a function of time t.

Answer 1

Given that: a = acceleration = (4i^ + 3j^) m/s^2

Using the following relations:
a = dv/dt
v = ∫ a dt

such that:
v = ∫ (4i^ + 3j^) dt + C
v = (4t + Cx)i^ + (3t + Cy)j^

Therefore:
Vx = 4t + Cx
Vy = 3t + Cy

At t = 0, Cx = Cy = 0

Finally:

Vx = 4t
Vy = 3t

Answer 2

The$\text{x}$ component of velocity as a function of time $\text{t}$ is $\boxed{{v_x} = 4t}$ and the $\text{y}$component of velocity as a function of time $\text{t}$ is $\boxed{{v_y} = 3t}.$

Further explanation:

Given:

The acceleration in xy plane is $a = 4.0\hat i + 3.0\hat j{\text{ m/}}{{\text{s}}^2}.$

Explanation:

At time $\text{t} = 0$ the particle is at rest.

The initial velocity of the particle is 0.

The given acceleration in xy plane is $a = 4.0\hat i + 3.0\hat j{\text{ m/}}{{\text{s}}^2}.$

The formula for the acceleration can be expressed as follows,

$a = \dfrac{{dv}}{{dt}}$

Solve the above equation,

$\begin{aligned}a\times dt &= dv\\\int {a \times dt} &= \int {dv} \\at &= v\\\left( {4\hat i + 3\hat j} \right)t &= v\\4t\hat i + 3t\hat j&= v\\\end{aligned}$

The$\text{x}$ component of velocity as a function of time $\text{t}$ is $\boxed{{v_x} = 4t}$ and the $\text{y}$ component of velocity as a function of time $\text{t}$ is $\boxed{{v_y} = 3t}.$

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736
2. Learn more about non-collinear brainly.com/question/4165000
3. Learn more about binomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Vectors

Keywords: particle, time, starts, rest, moves, plane, xy plane, acceleration, seconds, x component, y component, velocity, t = 0, function, function of time t.