An object starts from rest at x = 0 m and t = 0 s. It moves with a constant acceleration of 3 m/s² along x axis. What is its average velocity between time duration of 2 s and 4 s?

Concept:

Equation of motion:

• Equations of motion of kinematics describe the basic concept of the motion of an object such as the position, velocity, or acceleration of an object at various times.
• These three equations of motion govern the motion of an object in 1D, 2D, and 3D.
• Three equations: 
  1. v = u + at
  2. s = ut + 0.5 at²
  3. 2as = v² - u²
• Here, u = initial velocity, v = final velocity, s = displacement, t = time
• Under the influence of gravity, acceleration a is replaced by the acceleration due to gravity g.

Calculation:

Given,

Initial velocity, u = 0 m/s, Acceleration, a = 3 m/s²

From the first equation of motion, v = u + at

at t = 2 s, v = 0 + 3 × 2 = 6 m/s

So, the velocity is 6 m/s at t = 2 s.

From the second equation of motion,

s = ut + 0.5 at²

We need to calculate the displacement of the time interval (4 s to 2 s)

Now, s = (6 × 2) + (0.5 × 3 × 2²)

s = 18 m

The average velocity can be calculated as,

\(v_{avg}=\frac{total\, \, displacement}{total\, \, time\, duration}\)

\(v_{avg}=\frac{18}{2}=9~m/s\)

Hence, What is its average velocity between time 2 s and 4 s is 9 m/s.