Deceleratation plus reaction time problem

[bigman8424]

hard problem, a car traveling 95.0 km/hr needs to decelerate at 4.2m/sec/sec. reaction time of driver is 1.2 sec. what is original speed of driver in m/sec, total distance in m. needed to stop.

so the reaction distance + deceration distance what they're looking for

use this formula x1 = xo + vocost = ?

any thoughts

 

[Gokul43201]

bigman, read the rules for posting here. See your other thread.

 

[thepatientmental]

Based on the given information, we can approach this problem by first converting the initial speed of 95.0 km/hr to meters per second (m/s). To do this, we can use the formula m/s = (km/hr * 1000)/3600.

Using this formula, we can find that the original speed of the car in m/s is approximately 26.4 m/s.

Next, we can use the formula x1 = xo + v0cost to calculate the total distance needed to stop the car. Here, x1 represents the total distance, xo is the initial position (which we can assume to be 0), v0 is the initial velocity (26.4 m/s), c is the deceleration rate of 4.2 m/s^2, and t is the reaction time of 1.2 seconds.

Plugging in these values, we get x1 = 0 + (26.4 m/s)(1.2 s) + 0.5(4.2 m/s^2)(1.2 s)^2 = 31.68 m + 3.024 m = 34.704 m.

Therefore, the total distance needed to stop the car is approximately 34.704 meters.

In summary, the original speed of the car in m/s is 26.4 m/s and the total distance needed to stop the car is 34.704 meters. It is important for drivers to be aware of their reaction time and the deceleration rate of their vehicles, as it can greatly impact their ability to stop safely while driving.