Answer:
The width of the intersection is 20 meters
Step-by-step explanation:
The speed with which the cyclist is riding, v₁ = 6.20 m/s
The rate at which the car starts to accelerate, a = 3.844 m/s²
The initial velocity of the car = The car is stationary at the start = 0 m/s
The time at which the cyclist and the car reach the other side of the intersection = The same time;
Let 't' represent the time at which the cyclist and the car both reach the other side of the intersection, we have;
The distance travelled by the cyclist = The distance traveled by the car
∴ v₁ × t = 1/2 × a × t²
Plugging in the values for 'v₁', and 'a' in the above equation, we get;
6.20 × t = 1/2 × 3.844 × t²
∴ 1.922·t² - 6.20·t = 0
∴ t·(1.922·t - 6.20) = 0
t = 0, or t = 6.20/1.922 = 100/31
The time at which the cyclist and the car both reach the other side of the intersection, t = 100/31 seconds
The with of the intersection, w = v₁ × t
∴ w = 6.20 × 100/31 = 100/5 = 20
The width of the intersection, w = 20 meters.