An object starts from rest at x = 0 m and t = 0 s. It moves with constant acceleration 4 m/s2 along x axis. What is its average velocity between time 2 s and 6 s?

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RRB ALP Electrician 22 Jan 2019 Official Paper (Shift 3)
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  1. 18 m/s
  2. 12 m/s
  3. m/s
  4. 16 m/s

Answer (Detailed Solution Below)

Option 4 : 16 m/s
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Detailed Solution

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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:  v = u + at, s = ut + 0.5 at2, 2as = v2 - u2
  • Here, u = initial velocity, v = final velocity, s = displacement, t = time
  • Under the influence of gravity, acceleration a is replaced by acceleration due to gravity g.

Calculation:

Given,

Initial velocity, u = 0 m/s, Acceleration, a = 4 m/s2

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

at t = 2 s, v = 0 + 4 × 2 = 8 m/s

So, the velocity is 8 m/s at t = 2 s.

From the second equation of motion,

s = ut + 0.5 at2

We need to calculate the displacement of time interval (6 s to 2 s)

Now, s = 8 × 4 + 0.5 × 4 × 42

s = 64 m

The average velocity can be calculated as,

Hence, What is its average velocity between time 2 s and 6 s is 16 m/s.

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