College

Welcome to the article A particle moving in the horizontal direction has its position given by x t Find the expression for the velocity Ignore the pencil writing and. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!

A particle moving in the horizontal direction has its position given by x(t). Find the expression for the velocity.

Ignore the pencil writing and red pen, just answer the printed answer.

A particle moving in the horizontal direction has its position given by x t Find the expression for the velocity Ignore the pencil writing and

Answer :

The expression for the velocity is v(t) = 30m/s

Expression for the Velocity calculation

(a) x(t) = 30t

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 30t, we have:

v(t) = d/dt (30t)

= 30

So the expression for velocity is v(t) = 30 m/s.

(b) x(t) = 7sin(30)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 7sin(30), we have:

v(t) = d/dt (7sin(30))

= 7cos(30) * d/dt (30t)

= 3.5cos(30)

So the expression for velocity is v(t) = 3.5cos(30) m/s.

(c) x(t) = ecos(701)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = ecos(701), we have:

v(t) = d/dt (ecos(701))

= -e sin(701) * d/dt (701t)

= -701e sin(701t)

So the expression for velocity is v(t) = -701e sin(701t) m/s.

Learn more about differentiation here:

https://brainly.com/question/954654

#SPJ1

Thank you for reading the article A particle moving in the horizontal direction has its position given by x t Find the expression for the velocity Ignore the pencil writing and. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Brahmana

Final answer:

The expression for the velocity of a particle moving in the horizontal direction is given as v(t) = A + Bt¯¹. To find the acceleration, we can take the derivative of the velocity function with respect to time. The position of the particle at specific times can be found by integrating the velocity function.

Explanation:

To find the expression for the velocity of a particle moving in the horizontal direction, we can use the information given in the question. The velocity function is given as v(t) = A + Bt¯¹, where A = 2 m/s, B = 0.25 m, and 1.0 s ≤ t ≤ 8.0 s. To determine the acceleration, we can take the derivative of the velocity function with respect to time. We can then find the position of the particle at specific times using the relationship between position and velocity.

Step 1: Find the acceleration:

To find the acceleration, we can take the derivative of the velocity function. The derivative of v(t) = A + Bt¯¹ with respect to time is a(t) = 0 - B(-1)t¯². Simplifying this expression gives us a(t) = Bt¯².

Step 2: Find the position at t = 2.0 s:

To find the position of the particle at t = 2.0 s, we integrate the velocity function from t = 1.0 s to t = 2.0 s. The integral of v(t) = A + Bt¯¹ with respect to time is x(t) = At + (B/2)t². Plugging in the values A = 2 m/s and B = 0.25 m, we can calculate x(2.0) as follows: x(2.0) = 2(2.0) + (0.25/2)(2.0)² = 4.0 + 0.25(4.0) = 4.0 + 1.0 = 5.0 m.

Step 3: Find the position at t = 5.0 s:

To find the position of the particle at t = 5.0 s, we integrate the velocity function from t = 1.0 s to t = 5.0 s. Using the same integral from step 2, plugging in the values A = 2 m/s and B = 0.25 m, we can calculate x(5.0) as follows: x(5.0) = 2(5.0) + (0.25/2)(5.0)² = 10.0 + 0.25(25.0) = 10.0 + 6.25 = 16.25 m.