📘 Key Equations of Motion
🧠SECTION A: BASIC NUMERICALS (1–10)
Q1. A body starts from rest and accelerates at 2 m/s² for 5 s. Find final velocity.
Solution:
u = 0, a = 2, t = 5
v = u + at = 0 + (2×5) = 10 m/s
Q2. A car moving at 10 m/s accelerates at 3 m/s² for 4 s. Find final velocity.
Solution:
v = 10 + (3×4) = 22 m/s
Q3. Find displacement if u = 5 m/s, t = 4 s, a = 2 m/s².
Solution:
s = ut + ½at² = (5×4) + ½×2×16
= 20 + 16 = 36 m
Q4. A body reaches 20 m/s from rest in 4 s. Find acceleration.
Solution:
a = (v - u)/t = (20 - 0)/4 = 5 m/s²
Q5. A train accelerates uniformly from 5 m/s to 25 m/s in 10 s. Find acceleration.
Solution:
a = (25 - 5)/10 = 2 m/s²
Q6. A body starts with 10 m/s and moves with 2 m/s² for 5 s. Find displacement.
Solution:
s = 10×5 + ½×2×25
= 50 + 25 = 75 m
Q7. Find displacement when u = 0, a = 4 m/s², t = 3 s.
Solution:
s = ½×4×9 = 18 m
Q8. A body moving at 20 m/s comes to rest in 5 s. Find acceleration.
Solution:
a = (0 - 20)/5 = –4 m/s²
Q9. A car accelerates from 10 m/s to 30 m/s over 100 m. Find acceleration.
Solution:
v² = u² + 2as
900 = 100 + 2a×100
800 = 200a
a = 4 m/s²
Q10. A body moves from rest and travels 50 m in 5 s. Find acceleration.
Solution:
50 = ½ a×25
a = 4 m/s²
⚡ SECTION B: APPLICATION QUESTIONS (11–20)
Q11. A stone is dropped from rest. Find velocity after 3 s (g = 10 m/s²).
v = 0 + 10×3 = 30 m/s
Q12. A ball thrown upward with 20 m/s. Find time to reach highest point.
v = 0
0 = 20 – 10t
t = 2 s
Q13. A body travels 100 m in 10 s with constant acceleration from rest. Find acceleration.
100 = ½ a×100
a = 2 m/s²
Q14. A train increases speed from 10 m/s to 30 m/s in 5 s. Find distance.
s = 10×5 + ½×4×25
= 50 + 50 = 100 m
Q15. A body slows from 40 m/s to 10 m/s in 5 s. Find acceleration.
a = (10 - 40)/5 = –6 m/s²
Q16. A car travels 200 m in 10 s with acceleration 2 m/s². Find initial velocity.
200 = 10u + ½×2×100
200 = 10u + 100
u = 10 m/s
Q17. A body starts from rest and reaches 25 m/s in 5 s. Find displacement.
s = ½×5×25 = 62.5 m
Q18. A bike moving at 15 m/s stops in 3 s. Find stopping distance.
s = 15×3 + ½×(-5)×9
= 45 - 22.5 = 22.5 m
Q19. A body accelerates from 5 m/s at 3 m/s² for 4 s. Find final velocity.
v = 5 + 12 = 17 m/s
Q20. A body moves 80 m with acceleration 4 m/s² from rest. Find final velocity.
v² = 0 + 2×4×80 = 640
v = √640 = 25.3 m/s
🚀 SECTION C: HIGHER ORDER THINKING (21–30)
Q21. A car accelerates at 2 m/s² for 10 s. Find distance covered.
s = ½×2×100 = 100 m
Q22. A body moving at 20 m/s is retarded at 2 m/s². Find time to stop.
0 = 20 - 2t → t = 10 s
Q23. A body covers 150 m in 5 s with uniform acceleration. Find initial velocity if a = 4 m/s².
150 = 5u + ½×4×25
150 = 5u + 50
u = 20 m/s
Q24. A stone falls for 4 s. Find height fallen.
s = ½×10×16 = 80 m
Q25. A train moving at 30 m/s stops in 15 s. Find distance covered.
s = 30×15 + ½×(-2)×225
= 450 - 225 = 225 m
Q26. A car increases speed from 20 to 40 m/s in 10 s. Find acceleration.
a = 20/10 = 2 m/s²
Q27. A body covers 90 m in 6 s from rest. Find acceleration.
90 = ½ a×36
a = 5 m/s²
Q28. A body moving at 10 m/s accelerates to 50 m/s in 8 s. Find distance.
s = 10×8 + ½×5×64
= 80 + 160 = 240 m
Q29. A stone thrown downward at 5 m/s falls 45 m. Find final velocity.
v² = 25 + 2×10×45 = 925
v = 30.4 m/s
Q30. A body moving at 25 m/s stops after 50 m. Find retardation.
0 = 625 + 2a×50
a = –6.25 m/s²
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