A 3.50kg box is moving to the right with speed 8.00m/s on a horizontal, frictionless surface. At t = 0 a horizontal force is applied to the box. The force is directed to the left and has magnitude F(t)=( 6.00N/s2 )t2 Part A What distance does the box move from its position at t=0 before its speed is reduced to zero? Part B If the force continues to be applied, what is the velocity of the box at 3.50s ? Express your answer with the appropriate units.

2 answers
Question:

A 3.50kg box is moving to the right with speed 8.00m/s on a horizontal, frictionless surface. At t = 0 a horizontal force is applied to the box. The force is directed to the left and has magnitude F(t)=( 6.00N/s2 )t2
Part A
What distance does the box move from its position at t=0 before its speed is reduced to zero?
Part B
If the force continues to be applied, what is the velocity of the box at 3.50s ?
Express your answer with the appropriate units.

Answers

(a) The distance traveled by the box before stopping is 3.44 m.(b) The velocity of the box at 3.5 s is 40.55 m/s.The given parameters;mass of the box, m = 3.5 kgspeed of the box, v = 8 m/sforce applied to the box, F = (6 N/s²)t²The force applied on the box is given by Newton's second law of motion;[tex]F = ma\\\\F = \frac{mv}{t} \\\\\frac{dF}{dt} = mv\\\\F(t) = 6t^2\\\\\frac{dF}{dt} = 12 t\\\\12t = mv\\\\t = \frac{mv}{12} \\\\t = \frac{3.5 \times 8}{12} \\\\t = 2.33 \ s[/tex]The force applied to the box is calculated as;F = 6t²F = 6(2.33)²F = 32.57 NThe acceleration of the box is calculated as follows;[tex]a = \frac{F}{m} \\\\a = \frac{32.57}{3.5} \\\\a = 9.3 \ m/s^2[/tex]The distance traveled by the box before stopping is calculated as;[tex]v^2 = u^2 + 2as\\\\0 = u^2 + 2as\\\\-2as = u^2\\\\- s = \frac{u^2}{2a} \\\\-s = \frac{(8)^2}{2(9.3)} \\\\-s = 3.44 \ m\\\\|s| = 3.44 \ m[/tex]The velocity of the box at 3.5 s is calculated as;[tex]v_f = v_0+ at\\\\v_f = 8 + (9.3 \times 3.5)\\\\v_f = 40.55 \ m/s[/tex]Learn more here:https://brainly.com/question/18801986

Answer:F(t) = (-6.00 N/s^2)t^2 a(t) = (-3.00 N/s^2)t^2  Because F = ma, the acceleration function is the force function divided by mass (3.50 kg). Because the force is acting to the left, a negative has been introduced.  Take the integral of the acceleration function with the power rule for integrals. Initial velocity is 8.00 m/s ∫a(t) dt=v(t)+v1v(t)=(-1m/s^4)*t^3+9 m/sSetting velocity equal to zero and solving for t.  v(t)=0t^3=9s^3t=∛9s =2.08 sThe integral of velocity is position. The object begins at the origin so initial position is 0   ∫v(t) dt=  x(t)x(t)=(-0.25m/s^4)*t^4+(9m/s)*tPlugging the t from step 3 into the x(t) function from step 4. This is the answer to part a.  x(2.08)=14 mplug 3.50 s into the velocity function from step 2. Speed is the absolute value of velocity. This is the answer to part b.  v(3.5)=(1 m/s^4)(3.5 s)^3+9 m/s         = -18 m/sspeed(3.5 s)=║v(3.5)║=18 m/s

Similar Solved Questions

2 answers

See images attached, Brainliest to first and correct answer !

See images attached, Brainliest to first and correct answer !...
1 answer

Plz help I need to find one example of anecdotes, statistics and facts repetition,inclusive language,rhetorically questions,exaggeration Hyperbole, emotive language,stereotypes, alliteration, similes, metaphors and generalisation and explain what it makes the audience feel/do

Plz help I need to find one example of anecdotes, statistics and facts repetition,inclusive language,rhetorically questions,exaggeration Hyperbole, emotive language,stereotypes, alliteration, similes, metaphors and generalisation and explain what it makes the audience feel/do...
1 answer

For each domain, list one example of an organism that is found there.

For each domain, list one example of an organism that is found there....
1 answer

The radius of a circle is 5 in. Find its area to the nearest tenth. Answer: A = 1 in? Submit Answer​

The radius of a circle is 5 in. Find its area to the nearest tenth. Answer: A = 1 in? Submit Answer​...
1 answer

Make a list of four noble truths and eight fold paths of Bhuddhists​

Make a list of four noble truths and eight fold paths of Bhuddhists​...
1 answer

Can someone help me with A B and C ASAP ?? I’m struggling on finding the answers... I’ll give brainliest!! Please and ty !!

can someone help me with A B and C ASAP ?? I’m struggling on finding the answers... I’ll give brainliest!! Please and ty !!...
1 answer

What two numbers multiply to give 36 but add up to -13

what two numbers multiply to give 36 but add up to -13...
1 answer

If u answer i gives u my remaing poaints

if u answer i gives u my remaing poaints...
1 answer

What did the united states do with the philippines?

What did the united states do with the philippines?...
1 answer

In a much smaller model of the Gizmo apparatus, a 5 kg mass drops 86 mm (0.086 m) and raises the temperature of 1 gram of water 1°C. How much energy was transferred to the water? (Use a value of 9.8 m/s2 for g.)

In a much smaller model of the Gizmo apparatus, a 5 kg mass drops 86 mm (0.086 m) and raises the temperature of 1 gram of water 1°C. How much energy was transferred to the water? (Use a value of 9.8 m/s2 for g.)...
2 answers

What are the two uses for sugar in the recipe? To sweeten the batter; to throw away To sweeten the batter; to prevent stickiness To prevent stickiness; to throw away To prevent stickiness; toeat immediately

What are the two uses for sugar in the recipe? To sweeten the batter; to throw away To sweeten the batter; to prevent stickiness To prevent stickiness; to throw away To prevent stickiness; toeat immediately...
1 answer

Please answer this question for me. I’ll mark you as the brainliest. Find composite numbers that have the following characteristics (options in the photo).

Please answer this question for me. I’ll mark you as the brainliest. Find composite numbers that have the following characteristics (options in the photo)....
2 answers

According to Dr. K, what important role did trains play in the settlement of the West?

According to Dr. K, what important role did trains play in the settlement of the West?...
1 answer

Assume the current equilibrium level of income is $200 billion as compared to the full-employment income level of $240 billion. If the MPC is 0.625, what change in aggregate expenditures is needed to achieve full employment?

Assume the current equilibrium level of income is $200 billion as compared to the full-employment income level of $240 billion. If the MPC is 0.625, what change in aggregate expenditures is needed to achieve full employment?...
1 answer

Suppose that x and y vary inversely, and x = 2 when y = 9. Write the function that models the inverse variation

Suppose that x and y vary inversely, and x = 2 when y = 9. Write the function that models the inverse variation...
1 answer

PLEASE HELP !!! I WILL MARK U BRAINLY !

PLEASE HELP !!! I WILL MARK U BRAINLY !...
2 answers

What is the plural of thief?

What is the plural of thief?...
1 answer

Assume that A GHI ALMN. Which of the following congruence statements are correct? Check all that apply. A. GH = LM D B. 2N=2 C. G = LM O D. L=41 E. #ENM F. ME ZH

Assume that A GHI ALMN. Which of the following congruence statements are correct? Check all that apply. A. GH = LM D B. 2N=2 C. G = LM O D. L=41 E. #ENM F. ME ZH...
2 answers

What LCM of 9 and 21

What LCM of 9 and 21...
1 answer

An average ant is 1/4 inch long. An average aphid is 3/32 inch long. How many times longer is an average ant than an average aphid?

An average ant is 1/4 inch long. An average aphid is 3/32 inch long. How many times longer is an average ant than an average aphid?...

-- 0.010174--