derive the velocity as the function of time v(t) as one of the kinematics formulas of rectillinear motion with constant acceleration using integral caculuc
Answer (1)
Answer:[tex]v(t)=v_{o} +at[/tex]Acceleration is defined as the ratio between the change in velocity and the change in time.[tex]a=\frac{dv}{dt}[/tex]Since acceleration is constant, we can now rearrange the equation to get the velocity.[tex]dv=a(dt)[/tex]Proceed to integrate the function as a function of time.[tex]\int\ {dv} = \int\ a(dt)[/tex][tex]\int\ dv = a \int\ dt[/tex][tex]v(t) = at + C[/tex]Applying the initial condition where the initial velocity, t = 0;[tex]v_{0} = a_0 + C[/tex]Substitute the C, we get;[tex]v(t)=v_{0} +at[/tex]
