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2 years ago

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Sandy is on a road trip. She leaves at 8:00 AM. It takes her 2 hours to drive 200 kilometers. She stops at a rest stop for half

an hour. Then, she drives for 100 more kilometers, which takes her an hour and a half. What is Sandy's average velocity?

1 answer:

lutik1710 [3]2 years ago

0 0

The average velocity of Sandy is given by the total distance covered S divided by the total time taken t:
$v= \frac{S}{t}$

The total distance covered is
$S=200 km+0+100 km=300 km$
while the total time taken is 2 hours + half an hour (for the rest) + 1 hour and half, so
$t=2h+0.5h+1.5 h=4 h$
Therefore, the average velocity is
$v= \frac{S}{t}= \frac{300 km}{4 h}=75 km/h$

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Suppose a police officer is 1/2 mile south of an intersection, driving north towards the intersection at 40 mph. At the same tim

blagie [28]

Answer:

75.36 mph

Explanation:

The distance between the other car and the intersection is,

$x=x_{0}+V t \\ x=\frac{1}{2}+V t$

The distance between the police car and the intersection is,

$y=y_{0}+V t$

$y=\frac{1}{2}-40 t$

(Negative sign indicates that he is moving towards the intersection)

Therefore the distance between them is given by,

$z^{2}=x^{2}+y^{2}(\text { Using Phythogorous theorem })$

$z^{2}=\left(\frac{1}{2}+V t\right)^{2}+\left(\frac{1}{2}-40 t\right)^{2} \ldots \ldots \ldots(1)$

The rate of change is,

$2 z \frac{d z}{d t}=2\left(\frac{1}{2}+V t\right) V+2\left(\frac{1}{2}-40 t\right)(-40)$

$2 z \frac{d z}{d t}=V+2 V^{2} t-40+3200 t \ldots \ldots \ldots$

Now finding $z$ when $t=0,$ from (1) we have

$z^{2}=\left(\frac{1}{2}+V(0)\right)^{2}+\left(\frac{1}{2}-40(0)\right)^{2}$

$z^{2}=\frac{1}{4}+\frac{1}{4}=\frac{1}{2} \\ z=\sqrt{\frac{1}{2}} \approx 0.7071$

The officer's radar gun indicates 25 mph pointed at the other car then, $\frac{d z}{d t}=25$ when $t=0,$ from

From (2) we get

$2(0.7071)(25)=V+2 V^{2}(0)-40+3200(0)$

$2(0.7071)(25)=V+2 V^{2}(0)-40$

$35.36=V-40$

$V=35.36+40=75.36$

Hence the speed of the car is $75.36 mph$

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2 years ago

A hockey puck has a mass of 0.107 kg and is at rest. A hockey player makes a shot, exerting a constant force of 28.0 N on the pu

gregori [183]

Answer:

The speed does it head toward the goal = 41.87 $\frac{m}{s}$

Explanation:

Mass = 0.107 kg

Initial velocity ( u ) = 0

Force (F) = 28 N

Time = 0.16 sec

From newton's second law, Force = mass × acceleration

⇒ F = m × a

⇒ 28 = 0.107 × a

⇒ a = 261.7 $\frac{m}{s^{2} }$ --------- (1)

This is the value of acceleration.

Final speed of the mass is calculated by the equation V = U + at

⇒ U = 0 because mass in in rest position at start.

⇒ V = a t

Put the values of acceleration and time in above formula we get

⇒ V = 261.7 × 0.16

⇒ V = 41.87 $\frac{m}{s}$

Therefore the speed does it head toward the goal = 41.87 $\frac{m}{s}$

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Nadya [2.5K]

Answer:c

Explanation:

the rate of reaction increases as temperature increases

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GenaCL600 [577]

Around 70-72% of earth’s surface is covered in water (most of it is salt water).
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