Question

If a body moves in a straight line according to the law s = 24t + 3t2 - t3 , where s is the distance measured in meters from the origin and t is the time in seconds after it starts to move, calculate the body's velocity as a function of time. A. V = 30t - t2 B. V = 24 + 6t - 3t2 C. V = 24 + 3t - t2 D. V = 30t - 3t2

Answer 1

Remember that the velocity as a function of time is the derivative of the position as a function of time. 
To solve this we are going to take the derivative of our position function $s=24t+3t^2-t^3$. To do that er are going to apply the power rule of calculus: $\frac{dy}{dx} x^n=nx^{n-1}$

$\frac{dy}{dx} 24t+\frac{dy}{dx}3t^2-\frac{dy}{dx}t^3$
$24+2(3)t-3t^2$
$v=24+6t-3t^2$

We can conclude that the correct answer is: B. V = 24 + 6t - 3t2