Question

A particle's position along the x-axis is described by: x(t)=A t + B t​2 where t is in seconds, x is in meters, and the constants A and B are given.Randomized Variables A = -4.3 m/s B = 4.9 m/s​2 What is the velocity, in meters per second, of the particle at t​1 = 3.0 s?

Answer 1

The velocity of the particle at t = 3.0 s is 24.6 m/s.

Step-by-step explanation:

The velocity of the particle can be found by taking the derivative of the position function, x(t). In this case, x(t) = At + Bt², so the derivative is v(t) = A + 2Bt. Given that A = -4.3 m/s and B = 4.9 m/s², we can substitute these values into the derivative equation to find the velocity at t = 3.0 s.

Substituting t = 3.0 s, A = -4.3 m/s, and B = 4.9 m/s², we get v(3.0 s) = -4.3 + 2(4.9)(3.0) m/s = 24.6 m/s.

Therefore, the velocity of the particle at t = 3.0 s is 24.6 m/s.