Physics with Calculus
Which statement correctly matches the mathematical operation to the quantity being sought?
A student differentiates r→(t)=(5t2−4)i^+(9t−1)j^\(\overrightarrow{r}\)\(\left\)(t)\(\right\).=\(\left\)(5t^2-4\(\right\))\(\hat{i}\)+\(\left\)(9t-1\(\right\))\(\hat{j}\) and writes a→(t)=10i^+9j^\(\overrightarrow{a}\)\(\left\)(t)\(\right\).=10\(\hat{i}\)+9\(\hat{j}\). What is the correct acceleration vector?
A puck on an air table has acceleration a→(t)=(6t−4)i^+(3t2)j^\(\overrightarrow{a}\)\(\left\)(t)\(\right\).=\(\left\)(6t-4\(\right\))\(\hat{i}\)+\(\left\)(3t^2\(\right\))\(\hat{j}\) for 1≤t≤31 ≤ t ≤ 3 s. What is the change in velocity ΔvΔv over this interval?
A rescue craft moves so that a→(t)=(6t−2)i^+(4t3)j^\(\overrightarrow{a}\)\(\left\)(t)\(\right\).=\(\left\)(6t-2\(\right\))\(\hat{i}\)+\(\left\)(4t^3\(\right\))\(\hat{j}\), with v→(0)=−3i^+5j^\(\overrightarrow{v}\)\(\left\)(0\(\right\))=-3\(\hat{i}\)+5\(\hat{j}\) and r→(0)=2i^\(\overrightarrow{r}\)\(\left\)(0\(\right\))=2\(\hat{i}\). What is r→(t)\(\overrightarrow{r}\)\(\left\)(t\(\right\))?
If Δv=−9i^+12j^ m/s\(\Delta\) v=-9\(\hat{i}\)+12\(\hat{j}\)\(\text{ m/s}\), what is ∣Δv∣|Δv|?
