A motorist traveling at 17 m/s encounters a deer in the road 39 m ahead. If the maximum acceleration the vehicle’s brakes are capable of is −7 m/s 2 , what is the maximum reaction time of the motorist that will allow her or him to avoid hitting the deer? Answer in units of s. 019 (part 2 of 2) 10.0 points If his or her reaction time is 1.21983 s, how fast will (s) he be traveling when (s)he reaches the deer? Answer in units of m/s.
Answers
Answer:
1. t_reaction = 1.08 s
2. v₀₁ = 16.365 m/s
Explanation:
1. This is a kinematics exercise, let's analyze the situation a bit, we can calculate the braking distance and the rest of the distance we can use to calculate the reaction time.
Braking distance
v² = v₀² + 2 a x
when he finishes braking the speed is v = 0
0 = v₀² + 2 a x
x = -v₀² / 2a
x = - 17²/2 (-7)
x = 20.64 m
the distance for the reaction is
d = x_reaction + x
x_reaction = d - x
x_reaction = 39 - 20.64
x_reaction = 18.36 m
as long as it has not reacted the vehicle speed is constant
v = x_reaction / t_reaction
t_reaction = x_reaction / v
t_reaction = 18.36 / 17
t_reaction = 1.08 s
2. Let's find the distance traveled in the reaction time of t1 = 1.21983 s
as the speed is constant
v = x / t
x₁ = v t₁
the distance traveled during braking is
v² = v₀² + 2a x₂
0 = v₀² + 2 a x₂
x₂ = -v₀² / 2a
v = v₀
the total distance is
x_total = x₁ + x₂
x_total = v₀ t₁ + v₀² / 2a
39 = v₀ 1.21983 + v₀²/14
v₀² + 17.08 vo - 546 =0
we solve the second degree equation
v₀ = [ -17.08 ±√(17.08² + 4 546) ]/2
v₀ = [-17.08 ± 49.81 ]/2
v₀₁ = 16.365 m/s
v₀₂ = - 33.445 m/s
as the acceleration is negative the correct result is v₀₁ = 16.365 m/s
Related Questions
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A 5kg bowling ball is rolling with 75kg*m/s. How fast is it going?
Answers
Answer:
26.82m/s
Explanation:
Given
Mass = m= 0.4kg
Initial Velocity = u = 0
Charge = 4.0E-5C
Distance= d = 0.5m
Object Charge = 2E-4C
First, we'll calculate the initial energy (E)
E = Potential Energy
PE = kQq / d
Where k = coulomb constant = 8.99E9Nm²/C²
Energy is then calculated by;
PE = 8.99E9 * 4E-5 * 2E-4 / 0.5
PE = 143.84J
Energy = Potential Energy = Kinetic Energy
K.E = ½mv² = 143.84J
½mv² = ½ * 0.40 * v² = 143.85
0.2v² = 143.85
v² = 143.85/0.2
v² = 719.25
v = √719.25
v = 26.81883666380777
v = 26.82m/s
Hence, the object is 26.82m/s fast when the cart moving is very far (infinity) from the fixed charge
Answers
Answers
Answer:
a) 1 in. = 2.54 cm
Explanation:
Final answer:
The correct statement is a) 1 in. = 2.54 cm. To convert inches to centimeters, multiply the number of inches by the conversion factor 2.54 cm/1 in.
Explanation:
The correct statement is a) 1 in. = 2.54 cm.
To convert inches to centimeters, you can multiply the number of inches by the conversion factor 2.54 cm/1 in. For example, if you want to convert 7 inches to centimeters, you would multiply 7 in. by 2.54 cm/1 in. This gives you 17.78 cm, which is approximately equal to 17.68 cm (as stated in option b).
Option c) 1 ft = 12 in. and option d) 74 in. = 1 yd are also correct statements, but they are not directly related to the conversion between inches and centimeters.
Learn more about Conversion between inches and centimeters here:
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Answers
E=q/4πε₀ r²
here,r= 0.0075 m
q= 0.0035 C
1/4πε₀ = 9×10⁹
E= 9×10⁹× 0.0035/(0.0075)²
=5.6 ×10¹¹ N/C
Answer:
5.6x1011 N
Explanation:
I just got the wrong answer so here's the right one
Answers
Answer:
b. Decreases
Explanation:
The total resistance of a series circuit is equal to the sum of the individual resistances:
(1)
Therefore, as we add more lamps, the total resistance increases (because we add more positive tems in the sum in eq.(1).
The current in a circuit is given by Ohm's law:
where V is the voltage provided by the power source and is the total resistance. We notice that the current, I, is inversely proportional to the total resistance: therefore, when more lamps are added to the series circuit, the total resistance increases, and therefore the current in the circuit decreases.
Answers
Answer
To understand this concept it is necessary to understand Newton's Second Law
According to Newtons Second law applied force is equal to rate of change of momentum of a body.
Mathematically,
here, is rate of change of momentum with respect to time
It means If two eggs fall from same height,one on softer surface and other on hard surface that time the momentum of both eggs will remain equal at both the surfaces. But, impact time will be different. On hard surface egg will stop almost instantly so impact time will be small and hence the force on egg will be large therefore the egg will breakup.
On the other hand on the soft surface like a cotton, egg will not stop instantly but it will slow down for a few seconds and then stop due to which the time of impact will increase. Therefore the force on egg will be less and it won't break up.