CALC An object’s velocity is measured to be vx(t) = ? -

Step 1 of 3

Given that \(v_{x}(t)=\alpha-\beta t^{2}\)

We know that, \(v_{x \text { is the rate of change of displacement or }} v_{x}=\frac{d x}{d t}\).

So, \(\frac{d x}{d t}=\alpha-\beta t^{2}\) \(d x=\alpha d t-\beta t^{2} d t\)

Integrating this equation,

\(\begin{aligned}&\int_{0}^{x} d x=\int_{0}^{t} \alpha d t-\int_{0}^{t} \beta t^{2} d t \\&x=\alpha t-\beta t^{3} / 3\end{aligned}\)

Now, substituting the values of \(\alpha\) and \(\beta\) here.