Question

The position of a squirrel running in a park is given by r⃗ =[(0.280m/s)t+(0.0360m/s2)t2]i^+ (0.0190m/s3)t3j^.

What is υx(t), the x-component of the velocity of the squirrel, as function of time?

Answer 1

The x-component of the velocity of the squirrel as a function of time is υx(t) = 0.280m/s + (0.0720m/s²)t, obtained by differentiating the given position function with respect to time.

Step-by-step explanation:

To find the x-component of the velocity (υx(t)) of the squirrel as a function of time, we need to take the derivative of the x-component of the position function with respect to time. The given position function for the x-component is r(t) = (0.280m/s)t + (0.0360m/s²)t². Differentiating this with respect to time gives us:

υx(t) = d[(0.280m/s)t + (0.0360m/s²)t²]/dt

υx(t) = 0.280m/s + 2(0.0360m/s²)t

Thus, the x-component of the velocity of the squirrel as a function of time is υx(t) = 0.280m/s + (0.0720m/s²)t.