The[tex]\text{x}[/tex] component of velocity as a function of time [tex]\text{t}[/tex] is [tex]\boxed{{v_x} = 4t}[/tex] and the [tex]\text{y}[/tex]component of velocity as a function of time [tex]\text{t}[/tex] is [tex]\boxed{{v_y} = 3t}.[/tex]
Further explanation:
Given:
The acceleration in xy plane is [tex]a = 4.0\hat i + 3.0\hat j{\text{ m/}}{{\text{s}}^2}.[/tex]
Explanation:
At time [tex]\text{t} = 0[/tex] the particle is at rest.
The initial velocity of the particle is 0.
The given acceleration in xy plane is [tex]a = 4.0\hat i + 3.0\hat j{\text{ m/}}{{\text{s}}^2}.[/tex]
The formula for the acceleration can be expressed as follows,
[tex]a = \dfrac{{dv}}{{dt}}[/tex]
Solve the above equation,
[tex]\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}[/tex]
The[tex]\text{x}[/tex] component of velocity as a function of time [tex]\text{t}[/tex] is [tex]\boxed{{v_x} = 4t}[/tex] and the [tex]\text{y}[/tex] component of velocity as a function of time [tex]\text{t}[/tex] is [tex]\boxed{{v_y} = 3t}.[/tex]
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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.
