Question

The position vector $\overrightarrow{\mathbf{r}}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathit{t}\mathbf{}\hat{\mathbf{i}}\mathbf{+}\mathbf{(}\mathbf{e}\mathbf{t}\mathbf{+}\mathbf{f}{\mathbf{t}}^{\mathbf{2}}\mathbf{)}\widehat{\mathbf{}\mathbf{j}}$locates a particle as a function of time. Vector $\overrightarrow{\mathbf{r}}$is in meters, $\mathit{t}$is in seconds, and factors e and f are constants. Figure 4-31 gives the angle $\mathit{\theta }$of the particle’s direction of travel as a function of $\mathit{t}$($\mathit{\theta }$is measured from the positivedirection). What are (a) e, and (b) f, including units?

Short answer

Step-by-step solution

Given data

Understanding the instantaneous velocity

Instantaneous velocity may be defined as the rate of change of position of a particle with time.

The expression for the velocity is given as:

(a) Determination of the calue of e

Using equation (i), the velocity of the particle is,

(b) Determination of the value of f

The value of $\theta =0°$when $t=14.0\mathrm{s}$

Therefore,