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
Ede4ka [16]
2 years ago
8

The instantaneous speed of a particle moving along one straight line is v(t) = ate−6t, where the speed v is measured in meters p

er second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)
Physics
1 answer:
beks73 [17]2 years ago
5 0

Answer:

v_max = (1/6)e^-1 a

Explanation:

You have the following equation for the instantaneous speed of a particle:

v(t)=ate^{-6t}   (1)

To find the expression for the maximum speed in terms of the acceleration "a", you first derivative v(t) respect to time t:

\frac{dv(t)}{dt}=\frac{d}{dt}[ate^{-6t}]=a[(1)e^{-6t}+t(e^{-6t}(-6))]  (2)

where you have use the derivative of a product.

Next, you equal the expression (2) to zero in order to calculate t:

a[(1)e^{-6t}-6te^{-6t}]=0\\\\1-6t=0\\\\t=\frac{1}{6}

For t = 1/6 you obtain the maximum speed.

Then, you replace that value of t in the expression (1):

v_{max}=a(\frac{1}{6})e^{-6(\frac{1}{6})}=\frac{e^{-1}}{6}a

hence, the maximum speed is v_max = ((1/6)e^-1)a

You might be interested in
A 0.780 m long section of cable carrying current to a car starter motor makes an angle of 60.0° with the Earth's 5.50 ✕ 10−5 T f
STatiana [176]

Answer:

188 A

Explanation:

Parameters given:

Length of cable, L = 0.78 m

Angle, θ = 60º

Magnetic field, B = 5.5 * 10^(-5) T

Force experienced by wire, F = 7 * 10^(-3) N

The force experienced by a current carrying wire of length L, due to a magnetic field B is given as:

F = I * L * B * sinθ

=> I = F/(L * B * sinθ)

I = (7 * 10^(-3)) / (0.78 * 5.5 * 10^(-5) * sin60)

I = 188 A

6 0
3 years ago
Read 2 more answers
These the flow of electrons (the current) and where some of the electrons' energy gets converted into heat. (Lessons 5.01-5.03)
liq [111]

Answer:

Conductors.

Explanation:

Conductors allow the flow of electrons i. e. the current and where some of the electrons energy gets converted into heat while some electrons energy converted into light. Conductors are the materials which has the ability to allow heat and electricity to flow through them. Metals such as gold, copper, Silver, Aluminum, Mercury, Steel, Iron and salty water etc are good conductors of heat and electricity.

3 0
2 years ago
A truck loaded with sand accelerates along a highway. The driving force on the truck remains constant. What happens to the accel
pickupchik [31]

Answer:

Acceleration will increase.

Explanation:

The relation between force, mass and acceleration according to the Newton's second law of motion is given as:

F = ma

We are given that the driving force on the truck remains constant, so F is constant here. We can rewrite the above equation as:

a=\frac{F}{m}

Since, F is constant, the acceleration of the truck is inversely proportional to the mass.

There is a hole at the bottom of the truck through which the sand is being lost at a constant rate. Since, the sand is being lost, the overall mass of the truck is being reduced.

Since, the acceleration of the truck is inversely proportional to the mass, the reduced mass will result in an increased acceleration.

So, the acceleration of the truck will increase.

4 0
2 years ago
#3: a container has the dimensions of 30 cm x 50 mm x 0.2 m. the density of its contents is 2.5 g/cm3. what is the mass of the s
WARRIOR [948]
Good afternoon!

We calculate the volume of the container in cm³. To do that, we must put the units in cm:

30 cm → 30 cm
50 mm → 5 cm
0.2 m → 20 cm

The volume is:

V = 30 . 5 . 20

V = 3000 cm³

Now, we calculate the mas with the formula:

m = dV

m = 2.5 · 3000

m = 7500 g

Dividing by 1000, we have the mass in kg:


m = 7.5 kg
4 0
3 years ago
Read 2 more answers
Why was Dalton's atomic theory difficult for other scientists to accept? please help?!!!!!
Debora [2.8K]
It is cellmicktomic atoms
7 0
3 years ago
Other questions:
  • A weightlifter pulls on a 225 kg bar with 1600 N of force, but the bar does not move. How much work is performed?
    7·1 answer
  • A scientist studies the effect of adding different amounts of salt on the boiling point of water. He places his results in the g
    9·2 answers
  • What does a equal? 3/2 a -13=5​
    14·2 answers
  • The start-up procedure for a batch reactor includes a heating step where the reactor temperature is gradually heated to the nomi
    10·1 answer
  • If a water wave vibrates up and down three times each second and the distance between wave crests is 2 meters, what are:
    15·2 answers
  • A pulley is used to raise a heavy crate. With the pulley it only takes an effort force of 223 N to
    12·1 answer
  • A gas mixture has 10% O2, 50% Ar (40 gmw) and 40% Pu (244 gmw). What is the density of this mixture?
    8·1 answer
  • 1. You take a trip to Philadelphia to see a concert. Your older friend drives you there. The
    14·1 answer
  • Acceleration deceleration all rules
    6·1 answer
  • This graph shows the decomposition of hydrogen peroxide as it is exposed to air. Marty claims that the graph shows that the reac
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!