(a) The length of the train is 54.6 m
(b) The braking distance of the road train is 194.44 m
The given parameters:
acceleration of the car, a = 3.7 m/s²
initial velocity of the car, u = 30 m/s
final velocity of the car, v = 130 km/h = 36.11 m/s
To find:
The length of the train is the distance travelled by the car
The distance traveled by the car is calculated as:
[tex]v^2 = u^2 + 2as\\\\2as = v^2 - u^2\\\\s = \frac{ v^2 - u^2}{2a} \\\\where;\\\\s \ is \ the \ distance \ travelled \ by \ the \ car\\\\s = \frac{(36.11)^2 - (30)^2}{2\times 3.7} \\\\s = 54.585 \ m\\\\s \approx 54.6 \ m[/tex]
Thus, the length of the train is 54.6 m
(b) The braking distance of a road train travelling at 25 m s⁻¹
[tex]a = \frac{v_1^2}{2s_1} = \frac{v_2^2}{2s_2} \\\\Given;\\\\s_1 = 70 \ m\\\\v_1 = 15 \ m/s\\\\v_2 = 25 \ m/s\\\\s_2 = ?\\\\2s_2v_1^2 = 2s_1v_2^2\\\\s_2 = \frac{ 2s_1v_2^2}{2v_1^2} \\\\s_2 = \frac{s_1v_2^2}{v_1^2} \\\\s_2 = \frac{70\times 25^2}{15^2} \\\\s_2 = 194.44 \ m[/tex]
Thus, the braking distance of the road train is 194.44 m
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