Question

A particle moves according to the equation $x=5t^2+2t+5$ where $x$ is displacement and $t$ is time. Its average velocity in first $3$ seconds is

• A. $17m{s}^{-1}$
• B. $32m{s}^{-1}$
• C. $16m{s}^{-1}$
• D. None of these

Answer 1

Answer: (A)

$17m{s}^{-1}$

$u=\frac{dx}{dt}=10t+2$
avg. velocity=$\frac{{\int }_0^{t}u\left(t\right)dt}{{\int }_0^{t}dt}=\frac{{\int }_0^3(10t+2)dt}{3}$

$=\frac{\frac{(10t^2}{2}+2t){|}_0^3}{3}$

$=\frac{5\times 9+6}{3}=17m{s}^{-1}$