1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fiasKO [112]
3 years ago
6

The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t − 9, 0 ≤ t ≤ 3 (a) Find the

displacement. -9/2 Correct: Your answer is correct. m (b) Find the distance traveled by the particle during the given time interval.
Physics
1 answer:
Reil [10]3 years ago
4 0

Answer:

a) The displacement is -4.5 m.

b) The traveled distance is 11.7 m.

Explanation:

Hi there!

a)The velocity of the particle is the derivative of the displacement function, x(t):

v(t) = dx/dt = 5t - 9

Separating varibles:

dx = (5t - 9)dt

Integrating both sides from x = x0 to x and from t = 0 to t.

x - x0 = 1/2 · 5t² - 9t

x = 1/2 · 5t² - 9t + x0

If we place the origin of the system of reference at x = x0, the displacement at t = 3 will be x(3):

x(3) = 1/2 · 5 · (3)² - 9(3) + 0

x(3) = -4.5

The displacement at t = 3 s is -4.5 m. It means that the particle is located 4.5 m to the left from the origin of the system of reference at t = 3 s.

b) When the velocity is negative, the particle moves to the left. Let´s find the time at which the velocity is less than zero:

v = 5t - 9

0 > 5t - 9

9/5 > t

1.8 s > t

Then until t = 1.8 s, the particle moves to the left from the origin of the reference system.

Let´s find the position of the particle at that time:

x = 1/2 · 5t² - 9t

x = 1/2 · 5(1.8 s)² - 9(1.8 s)

x = -8.1 m

From t = 0 to t = 1.8 s the traveled distance is 8.1 m. After 1.8 s, the particle has positive velocity. It means that the particle is moving to the right, towards the origin. If at t = 3 the position of the particle is -4.5 m, then the traveled distance from x = -8.1 m to x = -4.5 m is (8.1 m - 4.5 m) 3.6 m.

Then, the total traveled distance is (8.1 m + 3.6 m) 11.7 m.

You might be interested in
The four principle surveying methods to spatially determine the position of features are: Select one: ut of a. triangulation, tr
Natalija [7]

A: perpendicular offset

B: radiation

C: transliteration

D: theodolite

7 0
3 years ago
The movement of the tectonic plates is caused by?
Sveta_85 [38]
The movement of the tectonic plates is caused by convection currents in Earth´s mantle.

Answer: A) convection currents in Earth´s mantle.
7 0
3 years ago
Read 2 more answers
A car traveling with constant speed travels 150 km in 7200s. What is the speed of the car?
LiRa [457]
Speed= distance/time
Speed= 150000m/7200s=20.83m/s(cor.to.2d.p.)
7 0
3 years ago
A 65 kg bungee jumper leaps from a bridge. She is tied to a bungee cord that is 12 m long when unstretched, and falls a total of
Nimfa-mama [501]

Answer:

(a) k = 30.33 N/m

(b) a = 9.8 m/s²

Explanation:

First, we need to find the force acting on the bungee jumper. Since, this is a free fall motion. Therefore, the force must be equal to the weight of jumper:

F = W = mg

F = (65 kg)(9.8 m/s²)

F = 637 N

(a)

Now applying Hooke's Law:

F = k Δx

where,

k = spring constant = ?

Δx = change in length of bungee cord = 33 m - 12 m = 21 m

Therefore,

637 N = k(21 m)

k = 637 N/21 m

<u>k = 30.33 N/m</u>

<u></u>

(b)

Since, this is free fall motion. Thus, the maximum acceleration will be the acceleration due to gravity.

a = g

<u>a = 9.8 m/s²</u>

7 0
3 years ago
Two 1.1 kg masses are 1 m apart (center to center) on a frictionless table. Each has +10 JC of charge. What is the initial accel
Katyanochek1 [597]

Answer:

The initial acceleration of the mass, if it is released and allowed to move = 0.8182\ m/s^2.

Explanation:

<u>Given:</u>

  • Mass of each object, \rm m = 1.1\ kg.
  • Charge on each object, \rm q = +10\ \mu C=+10\times 10^{-6}\ C.
  • Distance between the objects, \rm r=1\ m.

There are two forces that will act on these objects:

  1. Gravitational force due to masses of the objects, which is attractive.
  2. Electrostatic force due to the charges on the objects, which is repulsive because both the objects have positive charges.

The gravitational force between two masses \rm m_1 and \rm m_2, separated by distance \rm r is given by

\rm F_g = \dfrac{Gm_1m_2}{r^2}.

<em>where</em>,

G is the Universal Gravitational constant, having value = \rm 6.67\times 10^{-11}\ m^3kg^{-1}s^{-2}.

Therefore, the gravitational force between these masses is

\rm F_g=\dfrac{Gmm}{r^2}\\=\dfrac{(6.67\times 10^{-11})\times (1.1)\times (1.1)}{1^2}\\=8.0707\times 10^{-11}\ N.

The electrostatic force between two charges \rm q_1 and \rm q_2, separated by distance \rm r is given by

\rm F_e = \dfrac{kq_1q_2}{r^2}.

<em>where</em>,

k is the Coulomb's constant, having value = \rm 9\times 10^{9}\ C^2N^{-1}m^{-2}.

Therefore, the electrostatic force between these masses is

\rm F_e=\dfrac{kqq}{r^2}\\=\dfrac{(9\times 10^{9})\times (10\times 10^{-6})\times (10\times 10^{-6})}{1^2}\\=0.9\ N.

Since, one force is attractive and another is repulsive, therefore, the net force that one mass exerts on another is given by

\rm F=F_e-F_g\\=0.90-8.0707\times 10^{-11}\\=0.90\ N.

According to Newton's second law of motion,

\rm F=ma\\\\a\ is\ the\ acceleration\ of\ the\ mass.\\\rm\\\Rightarrow a = \dfrac Fm=\dfrac{0.90}{1.1}=0.8182\ m/s^2.

It is the acceleration with which the mass starts to move.

7 0
3 years ago
Other questions:
  • What happens to an electron when energy is added?
    5·1 answer
  • t or f if an object has a canstant acceleration it must ve changing velocity at the same rate over over again
    13·1 answer
  • When the tube is filled with mercury vapor, as in this case, a sharp drop in the collected current is observed when the accelera
    10·1 answer
  • What subtomic particle takes electric charge in friction​
    7·1 answer
  • Ice cream usually comes in 1.5 quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v
    15·1 answer
  • Suppose you are navigating a spacecraft far from other objects. The mass of the spacecraft is 2.6 × 104 kg (about 26 tons). The
    8·1 answer
  • A educação física, enquanto componente curricular da educação básica. Qual a tarefa que educação física?? Alguem me ajuda por fv
    10·1 answer
  • What happens at the end of most cold currents?​
    13·2 answers
  • 6
    7·1 answer
  • What is physical quantity?....​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!