Question

Velocity of a particle is given by \( v=\left(3 t^{2}+1\right) m / s \) if at \( t=1 \) its position is \( 2 m \) then find out its position at \( t=2 \) sec?

Answer 1

 \(v = 3t^2 + 1\)

\(\frac{dx}{dt}=3t^ 2+1\)

\(\int dx= \int^2_0 (3t^ 2+1)dt\)

\(r=[\frac{3t^ 3}{3}+t]^ 2_0\)

\(r=[3\times \frac{8}{3}+2]\)

x = 10m