Given the position function s(t), s(t) = t3 + 4t, where s is measured in meters and t is in seconds, find the velocity and acceleration of the particle at t = 2 seconds.

Velocity = 16 m/s

Acceleration = 12 m/s^2

Step-by-step explanation:

s(t) = t^3 + 4t

To find the velocity, differentiate s(t) with respect to t.

Velocity = s'(t)

Velocity = 3t^2 + 4

When t = 2

Velocity = 3(2)^2 + 4

= 3(4) + 4

= 12 + 4

= 16 m/s

To find the acceleration differentiate v(t) with respect to t.

acceleration = v'(t)

acceleration = 6t

When t = 2

acceleration = 6(2)

= 12 m/s^2

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

jeff jeff

step-by-step explanation: