In a 100 m linear accelerator, an electron is accelerated to 1.40% the speed of light in 35.0 m before it coasts 65.0 m to a target.

(b) How long does the total flight take?

Well, this electron must be in quite a hurry to get to its destination! It's like the electron version of Speedy Gonzales! Okay, let's calculate how long this speedy electron will take.

First, we need to find its speed before it starts coasting. We know that it is accelerated to 1.40% the speed of light, so we can calculate that to be:

Speed of light (c) = 3.00 x 10^8 m/s
Speed before coasting = 1.40% x c

Now, let's calculate the time it takes for the electron to travel the first 35.0 m:

Time for acceleration = Distance / Speed before coasting

And then the time it takes for the electron to coast the remaining 65.0 m:

Time for coasting = Distance / Speed before coasting (since its speed doesn't change)

Finally, to find the total flight time, we just add the time for acceleration and the time for coasting.

Total flight time = Time for acceleration + Time for coasting

Alright, let's crunch some numbers and figure out how fast this electron can reach its target!

To find the total flight time, we need to calculate the time spent in the acceleration region and the time spent in the coasting region separately, and then add them together.

First, let's calculate the time spent in the acceleration region.

We'll use the equation for time:
t = d / v

Where:
t = time
d = distance
v = velocity

In the acceleration region:
d = 35.0 m
v = 1.40% the speed of light

To convert the percentage of the speed of light to a decimal, we need to divide it by 100:
v = 1.40% / 100 = 0.014c (c = speed of light)

Now we can calculate the time in the acceleration region:
t1 = d / v
t1 = 35.0 m / 0.014c

Next, let's calculate the time spent coasting.

In the coasting region:
d = 65.0 m
v = 0.014c

Using the same equation:
t2 = d / v
t2 = 65.0 m / 0.014c

Finally, we can calculate the total flight time by adding the times for acceleration and coasting:
total flight time = t1 + t2

Now we can substitute the values and solve for the total flight time.

To find the total flight time of the electron in the linear accelerator, we need to calculate the time it takes for the electron to accelerate to 1.40% the speed of light and the time it takes for it to coast to the target.

First, let's calculate the time it takes for the electron to accelerate in the 35.0 m section of the linear accelerator.

We can use the equation for acceleration to find the time it takes for the electron to reach the desired speed. The equation is:

v = u + at

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

The initial velocity (u) of the electron is 0 since it starts from rest. The final velocity (v) is 1.40% of the speed of light, which we need to convert to meters per second. The speed of light is approximately 3.00 x 10^8 m/s.

1.40% of the speed of light = (1.40/100) * 3.00 x 10^8 m/s = 4.20 x 10^6 m/s

Next, we can calculate the acceleration (a) by using the equation:

a = (v - u) / t

Since the initial velocity (u) is 0, the equation simplifies to:

a = v / t

Rearranging the equation to solve for time (t), we have:

t = v / a

Substituting the values we have:

t = (4.20 x 10^6 m/s) / a

The acceleration (a) in a linear accelerator is constant. However, the given information does not provide the exact value of the acceleration. Without this value, we cannot calculate the exact time it takes for the electron to accelerate.

Therefore, to find the total flight time, we still need the exact value of the acceleration.