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 \(\boxed{{v_y} = 3t}.\)
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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.
