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Motion — Question 5

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Question 5

A stone is thrown in a vertically upward direction with a velocity of 5 ms-1. If the acceleration of the stone during its motion is 10 ms-2 in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

Answer

Given, initial velocity (u) = 5 ms-1

Terminal velocity (v) = 0

Acceleration = -10 ms-2 (as it is in upward direction)

According to the third equation of motion,

v2 – u2 = 2as

⇒s=v2−u22a\Rightarrow \text{s} = \dfrac{\text{v}^2 - \text{u}^2}{2\text{a}}

Substituting we get,

s = 0−522×−10=−25−20\dfrac{0 - {5}^2 }{2 \times -10} = \dfrac{-25}{-20} = 1.25 m.

Hence, distance covered = 1.25 m

According to the first equation of motion,

v = u + at

∴ time taken by the stone to reach a position of rest (maximum height) = v−ua\dfrac{\text{v} - \text{u}}{\text{a}}

Substituting we get,

0−5−10\dfrac{0-5}{-10} = 0.5 sec

∴ The stone reaches a maximum height of 1.25 m in 0.5 sec.

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Science | Chapter 7: MotionWeb Content — Quick Reference

Chapter 7: Motion — Quick Reference

distance displacement speed velocity acceleration equations of motion graphs circular motion

Quick Revision Points

  • Distance (scalar, total path) vs Displacement (vector, shortest path)
  • Speed = distance/time (scalar); Velocity = displacement/time (vector)
  • Acceleration a = (v−u)/t; unit: m/s²
  • Equations: v = u + at; s = ut + ½at²; v² = u² + 2as
  • d-t graph slope = speed; v-t graph slope = acceleration; area under v-t = distance
  • 1 km/h = 5/18 m/s; Free fall: u = 0, a = g = 9.8 m/s²
  • Uniform circular motion: constant speed, changing velocity (direction changes)
Exam Tips for Chapter 7
  • Read the detailed chapter notes for complete coverage of all NCERT topics.
  • Practice all NCERT in-text and back exercise questions — they are frequently asked in exams.
  • Focus on comparison tables, diagrams, and definitions — these are high-scoring areas.
  • For numericals (if applicable), practice at least 20 problems of varying difficulty.
  • Refer to the practice question bank (200+ questions) for thorough preparation.
Related Resources
  • Detailed Notes: ch07-motion.html
  • Practice Questions: 100+ questions with answers in 05-practice-questions/
  • Chapter Test: 30-mark test paper in 06-tests/chapter-tests-30marks/
  • Formula Sheet: Complete formula reference in 03-teacher-aid/formula-sheet.html
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