Question

If the speed of the particle is $v=4t^3-6t^2+5\text{m/s}$, the distance of the particle as a function of time $t$ is

• A. $\frac{4t^4}{3}-3t^3+5t\text{m}$
• B. $t^4-2t^3+5t\text{m}$
• C. $4t^4+6t^3-5t\text{m}$
• D. $t^4-3t^3+5t\text{m}$

Answer 1

The correct option is B $t^4-2t^3+5t\text{m}$

Given, the speed of the car is $v\left(t\right)=4t^3-6t^2+5$
So, the distance as a function of time is given as
$\int v\left(t\right)dt$
$\Rightarrow S=\int (4t^3-6t^2+5)dt=t^4-2t^3+5t\text{m}$