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1) An electron with initial velocity v0 = 2.6x10^5m/s enters a region 1.0 cm long where it is electrically accelerated (Figure 2-26). It emerges with velocity v = 4.70x10^6 m/s. What was its acceleration, assumed constant? (Such a process occurs in the electron gun in a cathode-ray tube, used in television receivers and oscilloscopes.)

I ended up getting 1.10 E 15 m/s^2 but I'm not sure if that's correct. I used the Vf^2-Vi^2=2ad equation.

2) You are arguing over a cell phone while trailing an unmarked police car by 36 m. Both your car and the police car are traveling at 110 km/h. Your argument diverts your attention from the police car for 2.5 s (long enough for you to look at the phone and yell, "I won't do that!"). At the beginning of that 2.5 s, the police officer begins emergency braking at 5 m/s2.

a) What is the separation between the two cars when your attention finally returns?

b) Suppose that you take another 0.4 s to realize your danger and begin braking. If you too brake at 5 m/s2, what is your speed when you hit the police car?

I found a similar problem online to this and just redid the work and changed my numbers but I'm stuck on part b. I'm not even sure if what I have for a is correct. My work is shown below:

distance between car and police= 36m speed of cars v=110km/hr =110(5/18) = 30.55m/s

after police car breaks: initial v=20.55m/s, final v= 0m/s, a=-5m/s^2 from V^2-V^2-2as

0^2-30.55^2=2(-5)s s=933.64/10= 93.364 m

velocity of police car after 2.5 secs of breaking v=v+at 30.55+(-5)2.5=18.05 m/s

distance traveled in this time by police is S: (18.05)^2-(30.55)^2-2(-5)s =60.78m

distance traveled by car in 2.5s=velocity x time: 30.55 x 2.5= 76.375m

separation between 2 cars: (36+60.78)-76.375= 20.405m

3) A car is driven east for a distance of 45 km, then north for 30 km, and then in a direction 35° east of north for 22 km. Sketch the vector diagram and determine the (a) magnitude and (b) angle of the car's total displacement from its starting point.

Here I tried to break the 3 distances into horizontal and vertical, which I thought was working but I ended up forgetting about the angle they give and now I'm totally confused. I'm not exactly sure how to find the magnitude nor the total displacement. I know you usually add up the distances to get the displacement but I have a feeling thats not what you do for this problem. Mind showing me the steps to these problems? Thanks