Let us apply the methodology discussed above to specific problems. These examples reflect the style and difficulty level found in Mathalino repositories and engineering board exams.
: ( v(t) = 20 e^-0.5 t ), ( v(3) \approx 4.46 , \textm/s ), total distance = 40 m .
At ( t = 0 ), ( s = 0 \Rightarrow C_2 = 0 ). Thus: [ \boxeds(t) = t^3 ]
This is the simplest and most common type. Here, ( a = \textconstant ). The equations of motion are: