An object starts from rest at x = 0 m and moves with a constant acceleration of 3 m/s² along the x-axis. During its journey from x = 13.5 m to x = 54 m, its average velocity is:

Question

Question

This question was previously asked in

RRB ALP Electronics Mechanic 21 Jan 2019 Official Paper (Shift 1)

Answer 1

The correct answer is 13.5 m/s.

Key Points

Given:
- Acceleration of the object, a = 3 m/s²
- Distance covered, d₁ = 13.5 m and d2 = 54 m
Find:
- Average velocity = V
Solution:
To calculate V, the formula used:
- v² - u² = 2 as
Third Law of Motion Equation here, v is the final velocity u is the initial velocity, i.e. u =0 m/s a is the acceleration s is the distance covered
Average velocity, V = (velocity at d1 + velocity at d2)/2
V = (v₁ + v₂)/2
Applying the 3rd law of motion equation formula:
For v1:
- v1² - u² = 2 x a x d1
- v1² - 0² = 2 x 3 x 13.5
- v1² = 81
- v1 = √81 = 9
- v1 = 9 m/s
For v₂:
- v₂2 - u2 = 2 x a x d2
- v22 - 0² = 2 x 3 x 54
- v22 = 324
- v2 = √324 = 18
- v2 = 18 m/s
Putting the value of v₁ and v₂ in equation 1:
V = (9 + 18)/2 = 27/2 = 13.5 V = 13.5 m/s

Hence, the average speed of the object is 13.5 m/s.