-The brakes on your automobile are capable of creating acceleration of 19 ft/s2. If you are going 76 mi/hr and suddenly see a state trooper, what is the minimum time required to get your car to 55 mi/hr?
For this answer, I got 1.62 s.
-How far do you travel while returning to the legal speed limit?
I have no idea how to get this answer.
Which equation can I use?
the formula that helps is: distance = v * t + (1/2)(a *t^2). Where a=acceleration, v=initial velocity, and t=time. Be very mindful of the sign for acceleration.
v is 76 mi/hr, right?
**Oops sorry, my sister was using this site last night for Chemistry.
76mi/hr= 111 ft/sec
55mi/hr=80.7ft/sec
Vf=Vi + at
80.7=111 - 19*t
t= 1.60 sec check that
avg velocity= (111+80.7)/2= 96.1ft/s
distance= avg velocity *time
Ok great, I get it now. Thanks!
To calculate the minimum time required to get your car from 76 mi/hr to 55 mi/hr, we can use the formula for acceleration:
Acceleration = (Final Velocity - Initial Velocity) / Time
In this case, the initial velocity is 76 mi/hr, the final velocity is 55 mi/hr, and we need to solve for time. Rearranging the formula, we have:
Time = (Final Velocity - Initial Velocity) / Acceleration
Plugging in the values, we get:
Time = (55 - 76) mi/hr / 19 ft/s^2
To compute the time, we first need to convert miles per hour (mi/hr) to feet per second (ft/s). Since 1 mile equals 5280 feet and 1 hour equals 3600 seconds, we can convert as follows:
Time = (55 - 76) mi/hr * (5280 ft/mi) * (1 hr / 3600 sec) / 19 ft/s^2
Simplifying the equation, we have:
Time = (-21 * 5280) / (19 * 3600) sec
Calculating the numerator and denominator, we get:
Time = -112,640 / 68,400 sec
Finally, dividing the values:
Time = -1.65 sec (rounded to the nearest hundredth)
Note: The negative sign indicates a deceleration, as you are slowing down.
Now, to find the distance traveled while returning to the legal speed limit, we can use the kinematic equation:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
In this case, the initial velocity is 55 mi/hr (since we are starting at this speed), the time is the value we just calculated (1.65 sec), and the acceleration is the given value of 19 ft/s^2. Again, we need to convert units to ensure they are consistent:
Distance = 55 mi/hr * (5280 ft/mi) * (1 hr / 3600 sec) * (1.65 sec) + (1/2) * 19 ft/s^2 * (1.65 sec)^2
Simplifying the equation, we have:
Distance = 128.67 ft + 23.4 ft
Therefore, the distance traveled while returning to the legal speed limit is approximately 152.07 ft.