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A car is approaching a stoplight. When the car is 200 m from the stoplight, the light turns yellow. The driver now has three seconds to either come to a stop, or hurry through the intersection before the light turns red. The car's initial velocity is 50 m/s, and it can accelerate at a maximum of 8 m/s^2. Determine if the car can make it through the light.

Respuesta :

  • Initial velocity=50m/s=u
  • Final velocity=v=0m/s
  • Acceleration=8m/s^2=a
  • Distance=s=200m

Apply third equation of kinematics

[tex]\\ \tt\hookrightarrow v^2-u^2=2as[/tex]

[tex]\\ \tt\hookrightarrow (50)^2=2(200)(8)[/tex]

[tex]\\ \tt\hookrightarrow 2500=16(200)[/tex]

[tex]\\ \tt\hookrightarrow 200=2500/16[/tex]

[tex]\\ \tt\hookrightarrow 200>156.25[/tex]

Unfortunately the car cannot make it through

fieryanswererft

Answer:

No. The car could not make through the light.

Explanation:

  • initial velocity is 50 m/s
  • can acceleration to 8 m/s²
  • Needs to cover 200 metres or more.
  • Has 3 seconds.

Formula: [tex]s=ut+\frac{1}{2} at^{2}[/tex]

where s is displacement, u is initial velocity, a is acceleration, t is time

Using the formula:

Distance: 50 * 3 + 1/2 * 8 * 3²

              : 186 meters

The car could not make it through.