Question

for time , the position of a particle moving along the -axis is given by . what is the acceleration of the particle when the velocity of the particle is ?

Answer 1

The position of a particle moving along the x-axis is given by x(t) = 4.0 + 2.0t m. (a) At what time does the particle cross the origin? (b) What is the displacement of the particle between t = 3.0 s and t = 6.0 s?

Step-by-step explanation:

The position of a particle moving along the x-axis is given by the function x(t) = 4.0 + 2.0t m.

(a) To find the time when the particle crosses the origin, we set x(t) = 0 and solve for t: 4.0 + 2.0t = 0. Solving this equation, we get t = -2.

(b) The displacement of the particle between t = 3.0 s and t = 6.0 s can be found by subtracting the values of x at these times:

x(6.0) - x(3.0)

= (4.0 + 2.0(6.0)) - (4.0 + 2.0(3.0))

= 12.0 m.