Question

An electron's position is given by vector r = 2.91t (i hat) - 4.01t2 (j hat) + 2.04 (k hat), with t in seconds and vector r in meters.
At t = 1.97 s, what is the magnitude of vector v?

Answer 1

Answer on Question #61625-Physics-Other

An electron's position is given by vector $r = 2.91t$ (i hat) - 4.01t² (j hat) + 2.04 (k hat), with t in seconds and vector r in meters.

At $t = 1.97$ s, what is the magnitude of vector v?

Solution

$$r = 2.91t \hat{i} - 4.01t^2 \hat{j} + 2.04 \hat{k}$$ $$v = \frac{dr}{dt} = 2.91 \hat{i} - 4.01(2t) \hat{j} + 0 \hat{k} = 2.91 \hat{i} - 8.02(t) \hat{j}$$ $$v(1.97) = 2.91 \hat{i} - 8.02(1.97) \hat{j} = 2.91 \hat{i} - 15.80 \hat{j}$$

The magnitude of vector v is

$$v = \sqrt{(2.91)^2 + (-15.80)^2} = 16.07 \frac{m}{s}.$$

Answer: $16.07 \frac{m}{s}$.

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