A driver traveling 50 mph rounds a bend and sees a car stopped 40 yards (36.576 m) ahead. Assumethe following: the road is flat
1 answer:
Answer:
a)there is collision
b)V=7.79m/s
Explanation:
A body that moves with constant acceleration means that it moves in "a uniformly accelerated movement", which means that if the velocity is plotted with respect to time we will find a line and its slope will be the value of the acceleration, it determines how much it changes the speed with respect to time.
When performing a mathematical demonstration, it is found that the equations that define this movement are as follows.
Vf=Vo+a.t (1)
{Vf^{2}-Vo^2}/{2.a} =X (2)
X=Xo+ VoT+0.5at^{2} (3)
X=(Vf+Vo)T/2 (4)
Where
Vf = final speed
Vo = Initial speed
T = time
A = acceleration
X = displacement
In conclusion to solve any problem related to a body that moves with constant acceleration we use the 3 above equations and use algebra to solve
To solve this problem, we use equation number 2 to calculate the distance traveled after the end of a movement with constant speed with a time of 0.2s, if it is less than 36.576m there is no collision.
Xt=X1+X2 (5)
X1= distance traveled with constant speed
X1=distance traveled with constant acceleration
for X1
X1=Vt
where
V=50mph=22.35m/s
t=0.2
X1=0.2x22.35m/s
X1=4.47m
for X2 using ecuation number 2
Vo=22.35m/s
Vf=0m/s
a=-6m/s^2
{Vf^{2}-Vo^2}/{2.a} =X
{0^{2}-22.35^2}/{(2).(6)} =X
x2=41.626m
Xt=x1+x2
Xt=41.626+4.47=49m
as the distance traveled is 49m the cars crash
b) to calculate the final speed we use the ecuation number tow(2)
X=36.576m
Vo=22.35m/s
a=-6m/s^2
{Vf^{2}-Vo^2}/{2.a} =X
solving for vf
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<u>Question 6:</u>
The density of gold is 19.3 g/cm³
The density of silver is 10.5 g/cm³
- The density of the substance in Crown A;
Density = mass ÷ volume = = 19.3 g/cm³
Since the density of gold, given, is 19.3 g/cm³ and the density of the substance in Crown A has a density of 19.3 g/cm³ , then that substance must be gold.
- The density of the substance in Crown B;
Density = mass ÷ volume = 1930 ÷ 184 = 10.48913043 g/cm³ ≈ 10.5 g/cm³ (answer rounded up to one decimal place)
Since the density of the substance in Crown B is approximately equal to 10.5 g/cm³ , then that substance is Silver.
- The density of substance in Crown C;
Density = mass ÷ volume = 1930g ÷ 150cm³ = 12.86666667 ≈ 12.9 cm³ (answer rounded up to one decimal place)
<h3><u>The density of the mixture:</u></h3><h3 />For 2 cm³ of the mixture, its mass equal 19.3 g + 10.5 g = 29.8 g
∴ for 1 cm³ of the mixture, its mass equal to = 14.9 g
Hence the density of the mixture = 14.9 g/cm³ and is not equal to the density of the substance in Crown C.
* Crown C is not made up of a mixture of gold and silver.
<u>Question 7:</u>
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- Water is poured into measuring cylinder until the liquid level is at the 100 cm³ mark.
- The total mass is now 850 g
The mass of water that occupied the 100 cm³ space of the container = total mass - mass of the empty container = 850 g - 500 g = 350 g
Density of the liquid (water) poured into the container = mass ÷ volume = 350 g ÷ 100 cm³ = 3.5g/cm³
<u>Question 8:</u>
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= 20 liters
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<u>Question 9:</u>
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<u>Question 10:</u>
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Answer:
Explanation:
Hi there,
To get started, recall the kinematic equations from either a textbook, equation sheet, etc. Kinematic equations are used when acceleration is <em>constant,</em> as stated in the prompt.
Best way to use kinematic equations is to see which variable you are looking for, then which variable is unknown to you and is not needed for that equation.
a) average velocity
Takes the form of:
this is the literal definition of average velocity; initial plus final divided by 2.
We know total displacement and total time elapsed, so we will use the middle form of the equation:
b) the final velocity
We can still use the average velocity formula, as the other two equations that include final velocity have acceleration variable which is unknown as of now.
Solve for final velocity:
this makes sense, since a velocity later in time is higher than a velocity earlier in time. It is increasing with increasing time because of acceleration.
c) the acceleration
There are two equations that can be used to solve this, but we will use the less time-consuming one, but both produce same answer:
Notice, change in velocity over change in time, and acceleration is constant. When acceleration is constant, it models a linear function, and acc. is just slope!
Study well and persevere. If you liked this solution, hit Thanks or give a rating!
thanks,