Given a constant acceleration and assuming linear motion, derive equations for velocity and position of a body with respect to time. Explain what the integration constant represents.

Respuesta :

Answer:

v = at + u

[tex]x = ut+\frac{1}{2}at^{2}+x_{0}[/tex]

Explanation:

acceleration, a = constant

As we know that acceleration is the rate of change of velocity

[tex]a=\frac{dv}{dt}[/tex]

[tex]dv=adt[/tex]

integrate on both sides

[tex]\int dv=\int adt[/tex]

v = at + u

Where, u is the integrating constant and here it is equal to the initial velocity

Now we know that the rate of change of displacement is called velocity

[tex]v = \frac{dx}{dt}[/tex]

[tex]dx=vdt=(u+at) dt[/tex]

Integrate on both sides

[tex]\int dx=\int (u+at) dt[/tex]

[tex]x = ut+\frac{1}{2}at^{2}+x_{0}[/tex]

where, xo is the integrating constant which is initial position of the particle.

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