A car is moving 60km/h when the driver sees a signal light 40m ahead turn red. The car can slow with acceleration -0.5g (where g=9.80m/s2). What is her stopping distance assuming
- A reaction time of 0.20s between when she sees the red light and when she hits the brake?
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eNotes policy only allows for one question per submission so I have editted your question accordingly. I have decided to demonstrate the more difficult question so if you understand these concepts, you should be able to answer the question assuming zero reaction time. If not, please post that question in another submission.
First, lets make all values in the same units so that we can easily perform dimensional analysis to find our solution. Let's first convert 60km/h to m/s by dimensional analysis (canceling out units by converting it to another unit of equivalent value. eg) 1000m=1km).
`(60km)/h *(1000m)/(1km)*(1h)/(3600s) ~~ 17m/s` = Speed of the Car
Since reaction time is 0.20s, we must calculate how far away from the red light the car actually is when the brakes are applied.
Distance When Brakes Are Applied=Distance When Driver Sees Red Light-(Speed of Car*Reaction Time)
`40m-(17m/s*0.20s)= 36.6m` away from light.
Now, let's find how long it takes for a 17m/s car to slow down to 0m/s.
Final Speed=Initial Speed + (Acceleration * Time)
Solving for Time:
`Time = (0m/s-17m/s)/(-0.5*9.8m/s^2)~~3.5s` to stop the car completely.
Now, calculate the distance traveled in 3.5s while decelerating at -4.9m/s^2 from 17m/s.
Distance = Initial Speed*Time + 1/2 * Acceleration * Time^2
`17m/s*3.5s + 1/2 * -4.9m/s^2 * (3.5s)^2 ~~29m ` to stop.
So depending on your reference point to the stopping distance:
From 40m away from red light, it takes `~~` 32.4m to stop. So the car will have completely stopped when it is 7.6m away from the red light. (I think this scenario is the one the creator of this question is thinking of.)
If we are talking about how far it takes for the car to stop once the brakes are applied, then it will take about 29m before the car comes to a complete halt.
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