Question

If the speed of a car is given as $v=4t-6\text{m/s}$, total displacement of the car in $10sec$ is

• A. $140\text{m}$
• B. $120\text{m}$
• C. $150\text{m}$
• D. $160\text{m}$

Answer 1

The correct option is A $140\text{m}$

Given, the speed of the car is $v\left(t\right)=4t-6$
and, displacement $S={\int }_0^{t}v\left(t\right)dt$
$\Rightarrow S={\int }_0^{10}(4t-6)dt=[2t^2-6t{]}_0^{10}$
$\Rightarrow S=(2\times {10}^2-6\times 10)-\left(0\right)=140\text{m}$