The instantaneous velocity \( v \) of a particle, starting with the initial velocity \( v_{0} \)...
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0The instantaneous velocity \( v \) of a particle, starting with the initial velocity \( v_{0} \) and moving with uniform acceleration \( a \), after time \( t \) is given by \( v=v_{0}+ \) at. Prove by integration that the displacement \( (x) \) at that particular instant from an arbitrary origin is
\[
x=x_{0}+v_{0} t+(1 / 2) a t^{2} \text {, }
\]
where \( x_{0} \) is the displacement at \( t=0 \).
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