Question

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.

Answer 1

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

Apply third equation of kinematics

`\\ \tt\hookrightarrow v^2-u^2=2as`

`\\ \tt\hookrightarrow (50)^2=2(200)(8)`

`\\ \tt\hookrightarrow 2500=16(200)`

`\\ \tt\hookrightarrow 200=2500/16`

`\\ \tt\hookrightarrow 200>156.25`

Unfortunately the car cannot make it through

Answer 2

No. The car could not make through the light.

Step-by-step explanation:

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

Formula:
`s=ut+(1)/(2) at^(2)`

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.