Question

If the speed of a car is given as $v=3t^2+2t+3\text{m/s}$, total distance covered by the car in $10sec$ is

• A. $1230\text{m}$
• B. $1030\text{m}$
• C. $930\text{m}$
• D. $1130\text{m}$

Answer 1

The correct option is D $1130\text{m}$

Given, the speed of the car is $v\left(t\right)=3t^2+2t+3$
and, distance $S={\int }_0^{t}v\left(t\right)dt$
$\Rightarrow S={\int }_0^{10}(3t^2+2t+3)dt=[t^3+t^2+3t{]}_0^{10}$
$\Rightarrow S=({10}^3+{10}^2+3\times 10)-\left(0\right)=1130\text{m}$