Set up the problem with the conversion rates as fractions where when you multiply the units cancel out leaving the desired units behind.
a = 3.09 m/s²
<h3>Explanation</h3>
This question doesn't tell anything about how long it took for the car to go through 105 meters. As a result, the <em>timeless </em>suvat equation is likely what you need for this question.
In the <em>timeless</em> suvat equation,
where
is the acceleration of the car;
is the <em>final</em> velocity of the car;
is the <em>initial</em> velocity of the car; and
is the displacement of the car.
Note that <em>v</em> and <em>u</em> are velocities. Make sure that you include their signs in the calculation.
In this question,
Apply the <em>timeless</em> suvat equation:
.
The value of is greater than zero, which is reasonable. Velocity of the car is negative, meaning that the car is moving backward. The car now moves to the back at a slower speed. Effectively it accelerates to the front. Its acceleration shall thus be positive.
Answer:27 km per hour West + 17 km per hour North
This is an interesting (read tricky!) variation of Rydberg Eqn calculation.
Rydberg Eqn: 1/λ = R [1/n1^2 - 1/n2^2]
Where λ is the wavelength of the light; 1282.17 nm = 1282.17×10^-9 m
R is the Rydberg constant: R = 1.09737×10^7 m-1
n2 = 5 (emission)
Hence 1/(1282.17 ×10^-9) = 1.09737× 10^7 [1/n1^2 – 1/25^2]
Some rearranging and collecting up terms:
1 = (1282.17 ×10^-9) (1.09737× 10^7)[1/n2 -1/25]
1= 14.07[1/n^2 – 1/25]
1 =14.07/n^2 – (14.07/25)
14.07n^2 = 1 + 0.5628
n = √(14.07/1.5628) = 3
;
; and
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