The position of a particle moving along x axis is given in cm by $\mathbf{x}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{75}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{50}{\mathbf{t}}^{\mathbf{3}}$, where t is in seconds. Calculate (a) the average velocity during time interval t=2 s to t=3 s; (b) the instantaneous velocity at t=2 s; (c) the instantaneous velocity at t=3s; (d) the instantaneous velocity at t=2.5 s; (e) the instantaneous velocity when the particle is midway between its positions at t=2 s and t=3 s (f) Graph x vs. t and indicate your answers graphically.

Figure shows a red car and a green car that move toward each other. The other figure is a graph of their motion, showing their positions ${\mathbf{x}}_{\mathbf{g}\mathbf{0}}\mathbf{=}\mathbf{270}\mathbf{m}$ and ${\mathbf{x}}_{\mathbf{r}\mathbf{0}}\mathbf{35}\mathbf{m}\mathbf{=}\mathbf{-}\mathbf{}$ at time $\mathbf{t}\mathbf{=}\mathbf{0}$.The green car has a constant speed of 20.0 m/s and the red car begins from rest. What is the acceleration magnitude of the red car?

Suppose that a passenger intent on lunch during his first ride in a hot-air balloon accidently drops an apple over the side during the balloon’s liftoff. At the moment of the apple’s release, the balloon is accelerating upward with a magnitude of $\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$ and has an upward velocity of 2 m / s magnitude . What are the (a) magnitude and (b) direction of the acceleration of the apple just after it is released? (c) Just then, is the apple moving upward or downward, or is it stationery? (d) What is the magnitude of its velocity just then? (e) In the next few moments, does the speed of the apple increase, decrease, or remain constant?

The speed of a bullet is measured to be ${}^{\mathbf{640}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}}$ as the bullet emerges from a barrel of length ${}^{\mathbf{1}\mathbf{.}\mathbf{20}\mathbf{}\mathbf{m}}$. Assuming constant acceleration, find the time that the bullet spends in the barrel after it is fired.

You are arguing over a cell phone while trailing an unmarked police car by $\mathbf{25}\mathbf{\hspace{0.33em}}\mathbf{m}$; both your car and the police car are traveling at $\mathbf{110}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{h}\mathbf{.}$ .Your argument diverts your attention from the police car for $\mathbf{}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\hspace{0.33em}}\mathbf{s}$, (long enough for you to look at the phone and yell, “I won’t do that!”). At the beginning of that $\mathbf{}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\hspace{0.33em}}\mathbf{s}$,the police officer begins braking suddenly at $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$(a)What is the separation between the two cars when your attention finally returns? Suppose that you take another $\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{}\mathbf{s}$ to realize your danger and begin braking. (b)If you too brake at $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$ ,what is your speed when you hit the police car?

You are to drive 300km to an interview. The interview is at 11.15 AM. You plan to drive at 100 km/h , so you leave at 8 AM, to allow some extra time. You drive at that speed for the first 100 km, but then construction work forces you to slow to 40 km/h for 40km. What would be the least speed needed for the rest of the trip to arrive in time for the interview?