Question

A body fell down from rest and is falling down with an acceleration 10 m/s². When it was hitting the ground, its displacement was 20 m. The velocity with which it hits the ground is:

• A. 5 m/s
• B. 10 m/s
• C. 15 m/s,
• D. 20 m/s

Answer 1

Answer:

D. 20 m/s

Understanding Motion Under Constant Acceleration

• This problem involves a body undergoing uniformly accelerated motion, specifically falling under gravity.
• The key to solving such problems is identifying the known quantities and selecting the appropriate equation of motion.

Given Parameters:

• Initial velocity (u) = 0 m/s (since the body fell from rest).
• Acceleration (a) = 10 m/s² (given). This is often approximated as the acceleration due to gravity (g) for simplification in competitive exams.
• Displacement (s) = 20 m.

Applying the Equation of Motion:

• The most suitable kinematic equation that relates initial velocity (u), final velocity (v), acceleration (a), and displacement (s) is: v² = u² + 2as.
• Substituting the given values into the equation:
  • v² = (0)² + 2 × 10 m/s² × 20 m
  • v² = 0 + 400 m²/s²
  • v² = 400 m²/s²
  • v = √400 m²/s²
  • v = 20 m/s
• Therefore, the velocity with which the body hits the ground is 20 m/s.

Key Facts for Competitive Exams:

• There are three primary equations of motion for uniformly accelerated linear motion:
  1. v = u + at (Velocity-time relation)
  2. s = ut + ½at² (Position-time relation)
  3. v² = u² + 2as (Position-velocity relation)
• For objects falling freely under gravity, the acceleration 'a' is replaced by 'g' (acceleration due to gravity), which is approximately 9.8 m/s² or often taken as 10 m/s² for calculation simplicity in exams.
• When a body falls from rest, its initial velocity (u) is always 0.
• The direction of acceleration due to gravity (g) is always downwards, towards the center of the Earth.
• Air resistance is generally neglected in these types of ideal physics problems unless specified.