All categories

3 years ago

The position of a particle is given by ~r(t) = (3.0 t2 ˆi + 5.0 ˆj j 6.0 t kˆ) m

Physics

1 answer:

Julli [10]3 years ago

5 0

Answer:

$v=(6ti+6k)\ m/s$

Explanation:

Given that,

The position of a particle is given by :

$r(t) = (3.0 t^2 i + 5.0j+ 6.0 tk) m$

Let us assume we need to find its velocity.

We know that,

$v=\dfrac{dr}{dt}\\\\=\dfrac{d}{dt}(3.0 t^2 i + 5.0j+ 6.0 tk) \\\\=(6ti+6k)\ m/s$

So, the velocity of the particle is $(6ti+6k)\ m/s$ .

You might be interested in

A cross-country skier moves 36 meters eastward, then 44

ivanzaharov [21]

Answer:

Magnitude = 14 metres

Direction = eastward.

Explanation:

A cross-country skier moves 36 meters eastward, then 44meters westward, and finally 22 meters eastward.

Whats the Magnitude and Direction?

The magnitude and direction will be the displacement of the cross country skier.

Let the east ward be positive and the west ward be negative.

Since the skier moves 36 meters eastward, then 44meters westward, and finally 22 meters eastward. Then, that will be:

36 - 44 + 22 = 14

Since the answer is positive, the magnitude is 14 and the direction is east ward.

3 0

3 years ago

A girl pushes a 1.04 kg book across a table with a horizontal applied force 10 points

mr Goodwill [35]

Answer:

Approximately $11.0\; \rm m \cdot s^{-1}$ . (Assuming that $g = 9.81 \; \rm N \cdot kg^{-1}$ , and that the tabletop is level.)

Explanation:

Weight of the book:

$W = m \cdot g = 1.04 \; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \approx 10.202\; \rm N$ .

If the tabletop is level, the normal force on the book will be equal (in magnitude) to weight of the book. Hence, $F(\text{normal force}) \approx 10.202\; \rm N$ .

As a side note, the $F_N$ and $W$ on this book are not equal- these two forces are equal in size but point in the opposite directions.

When the book is moving, the friction $F(\text{kinetic friction})$ on it will be equal to

$\mu_{\rm k}$ , the coefficient of kinetic friction, times
$F(\text{normal force})$ , the normal force that's acting on it.

That is:

$\begin{aligned}& F(\text{kinetic friction}) \\ &= \mu_{\rm k}\cdot F(\text{normal force})\\ &\approx 0.35 \times 10.202\; \rm N \approx 3.5708\; \rm N\end{aligned}$ .

Friction acts in the opposite direction of the object's motion. The friction here should act in the opposite direction of that $15.0\; \rm N$ applied force. The net force on the book shall be:

$\begin{aligned}& F(\text{net force}) \\ &= 15.0 \; \rm N - F(\text{kinetic friction}) \\& \approx 15.0 - 3.5708\; \rm N \approx 11.429\; \rm N\end{aligned}$ .

Apply Newton's Second Law to find the acceleration of this book:

$\displaystyle a = \frac{F(\text{net force})}{m} \approx \frac{11.429\; \rm N}{1.04\; \rm kg} \approx 11.0\; \rm m \cdot s^{-2}$ .

6 0

3 years ago

Please the organisms in the order of transmission for Lyme disease. Begin with the organism that originally carries the bacteria

Aleonysh [2.5K]

White footed mouse, than human.

5 0

3 years ago

1. A 9000 kg van was stopped at a traffic light when it rear-ended with an 850 compact car moving to the east at a velocity of 5

____ [38]

Answer:

1.785 m/s

Explanation:

The momentum can be calculated using the expression below

M1 *V1 + M2 * V2 = (M1+M2) V3

M1= mass of van=9000 kg

M2= mass of car= 850kg

V3= velocity of entangled car

V1= Velocity of the van= 0

V2= velocity of the car= 5 m/ s

Substitute the values

(900×0) + (500×5)=( 900+500)× V3

2500=1400 V3

V3=2500/1400

V3= 1.785 m/s

Hence, velocity of the entangled cars after collision is 1.785 m/s

8 0

2 years ago

Answer the following question: “Do the particles in a gas ever slow down and stop? Include information about the three states of

jarptica [38.1K]

Answer:

I hope it is no too late

Explanation:

hmmm,

In a gas, for example, the molecules are traveling in random directions at a variety of speeds - some are fast and some are slow. ... If more energy is put into the system, the average speed of the molecules will increase and more thermal energy or heat will be produced.

3 0

3 years ago