Physics, 04.07.2020 14:01 Kana81

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 4 (a) Find the velocity at time t. v(t) = m/s (b) Find the distance traveled during the given time interval. m

Answers: 2

Show answers

Answers

Answer from: alexisbarry2398

We want to get the motion equations for a particle, given that we know its acceleration and its initial velocity.

a) v(t) = (1m/s^3)*t^2 + (2m/s^2)*t - 3m/s

b) the distance traveled in that interval is 25.33 meters.

-------------------------

Let's see how to et the solutions:

a) We want to find the velocity equation, to get it, we can just integrate the acceleration equation such that the constant of integration will be the initial velocity.

The acceleration equation is:

a(t) = (2m/s^3)*t + 2m/s^2

To get the velocity we integrate:

v(t) = (1/2)*(2m/s^3)*t^2 + (2m/s^2)*t + v_0

Where v₀ is the initial velocity, which we know is -3m/s

Then the velocity equation is:

v(t) = (1m/s^3)*t^2 + (2m/s^2)*t - 3m/s

b) Now we want to find the distance traveled in the interval 0s ≤ t ≤ 4s

Then first we need to get the position equation, to do it we need to integrate the velocity equation.

p(t) = (1/3)*(1m/s^3)*t^3 + (1/2)*(2 m/s^2)*t^2 - (3m/s)*t

Where the constant of integration is ignored because we want to compute a difference.

The distance traveled in that interval is given by:

p(4s) - p(0s) = p(4s) = (1/3)*(1m/s^3)*(4s)^3 + (1/2)*(2 m/s^2)*(4s)^2 - (3m/s)*4s = 25.33m

If you want to learn more, you can read:

link

Answer from: iamabeast51

V(t) = 2t^2 + 2t - 3

$\Delta S = 46.667\ m$

Explanation:

We can find the velocity at time t using the formula:

V(t) = V(0) + a*t

Where V(t) is the velocity at time t, V(0) is the inicial velocity and a is the acceleration.

Then we have that:

V(t) = -3 + (2t+2)*t

V(t) = 2t^2 + 2t - 3

If we integrate the velocity in the time, we find the displacement (distance traveled):

$\int {V(t)} \, dt = 2t^3/3 + t^2 - 3t + c$

$\Delta S = \int\limits^4_0 {V(t)} \, dt = (2*4^3/3 + 4^2 - 3*4) - (2*0^3/3 + 0^2 - 3*0)$

$\Delta S = 46.667\ m$

Answer from: Quest

Is a vector quantity that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

Answer from: Quest

It is d, all the other ones say incorrect answer .

Another question on Physics

Physics, 22.06.2019 14:00

Me pl give an example of a collision in real life. use the law of conservation of energy to describe the transfer of momentum. be sure and discuss the momentum before and after the collision occurs. you will need at least 3 sentences to thoroughly answer this question.

Answers: 3

Answer

Physics, 22.06.2019 18:30

En un laboratorio, nakisha mezcla una solución de hidróxido de sodio con un indicador llamado fenolftaleína. cuando se combinan, crean una solución de color rosa. nakisha se pregunta si la mezcla de otras soluciones con fenolftaleína también creará este color rosa. ? cómo podría nakisha utilizar el proceso de investigación científica para determinar si la mezcla de otras soluciones con fenolftaleína también creará un color rosa? marque las que correspondan.

Answers: 2

Answer

Physics, 22.06.2019 22:30

Use the illustration to describe how the electromagnetic spectrum changes as its frequency moves from radio waves to higher energy gamma waves in terms of wavelength and amplitude.

Answers: 1

Answer

Physics, 23.06.2019 08:30

Which is gerrymandering a problem for the house of representatives but not the senate? a.) members of the house are greatly influenced by their political parties. b.) senators serve longer terms than members of the house. c.) members of the house are more influenced by changes in public opinion. d.) senators are elected in statewide elections rather than in specific districts.

Answers: 1

Answer

You know the right answer?

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving al...

Questions