Stopping Distance: Estimate the stopping distance of a vehicle initially traveli

Question

Stopping Distance: Estimate the stopping distance of a vehicle initially traveling at 50 mph (=22.4 m/s) in the + x direction. Assume the driver is paying attention and has a reaction time of 0.5s. and the vehicle accelerates at a=-6.0 m/s. Assume that the vehicle is in ideal working order, on dry pavement and does not slide. Typical reaction times can vary from 0.3s to in excess of 3.0s depending on the state of the driver.Typical acceleration for stopping, range from 5.0 m/s^2 to 8.0 m/s^2.

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Explanation / Answer

Determine the speed the car is traveling--the higher the speed, the greater the braking distance. For this example, a speed of 50 miles per hour will be used.

Establish the stopping distance. This is the distance from your car to the object in front of it.

First calculate the distance travelled in 0.5 secs

S= 22.4*0.5+1/2*6*0.52 =11.95 m

Institute a deceleration rate. This is the rate that applying the brakes slows the vehicle. This rate is typically 5.0 to 8.0 m/sec2

V^2 = u^2 + 2 as
^2 means square
Here,final velocity of car should be zero as it comes to rest,ie V=0
Initial velocity, u = 30m/s
Acceleration, a = -7 m/s^2 ( negative because the car is decelarating )
Distance we have to find,S = ?
Equation becomes,
0^2 = (30)^2 + 2*-7 *S
0 = 900 -14 S
ie
14 S = 900
S = 900/ 14 = 64.28 meters

Ascertain the thinking distance, which is reaction time as it relates to distance. Reaction time can take an average of 2 seconds to set in and realize that there is a problem. The reaction time can vary given the age of the driver, condition of the car, distraction in the vehicle and condition of the road.

Calculate the total braking distance. This formula is 1/2 the initial velocity in feet per second multiplied by the time required to stop,

Total stopping distance = 11.95 m+ 64.28 m = 76.23 m

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