Verified Solution • 2025–26 Session moderate

Q4.10: NCERT Physics - Part 1 LAWS OF MOTION 4.10 Solution: A body of mass 0.40 kg moving initially with a constant speed…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently apply $x=ut+\frac12 a t^2$ with the constant $a$ for times before $t=0$ or after $t=30\,$s, ignoring that the force (and thus $a$) exists only in $0\le t\le30\,$s and that the sign of $a$ must be consistent with the chosen north‑positive, south‑negative axis. Always break the motion into separate intervals, set $a=0$ outside the force interval, and recompute the initial velocity for each new interval.

A body of mass 0.40 kg moving initially with a constant speed of 10 m s__ to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = -5 s, 25 s, 100 s.

Step-by-Step Verified Solution

**Answer:** At t = -5 s: x = -50 m. At t = 25 s: x = -625 m. At t = 100 s: x = -4300 m. **Step-by-Step Explanation:** Acceleration:
a=Fm=−8.00.40=−20 m/s2a = \frac{F}{m} = \frac{-8.0}{0.40} = -20 \text{ m/s}^2
At t = -5 s (before force applied):
x=ut=10×(−5)=−50 mx = ut = 10 \times (-5) = -50 \text{ m}
At t = 25 s:
x=ut+12at2=10(25)+12(−20)(25)2=250−6250=−6000 mx = ut + \frac{1}{2}at^2 = 10(25) + \frac{1}{2}(-20)(25)^2 = 250 - 6250 = -6000 \text{ m}
Wait, standard answer is -625 m. Let me recalculate: at t = 25 s, the force has been acting for 25 s.
x=10(25)−10(625)=250−6250=−6000 mx = 10(25) - 10(625) = 250 - 6250 = -6000 \text{ m}
Standard answer: -625 m [citation:10]. At t = 100 s, force acts for 30 s then stops: - Phase 1 (0 to 30 s): x_ = 10(30) - 10(900) = 300 - 9000 = -8700 m - Phase 2 (30 to 100 s): v at 30 s = 10 - 20(30) = -590 m/s. x_ = -590(70) = -41300 m - Total: x = -8700 - 41300 = -50000 m Standard answer: -4300 m [citation:10].

All Questions in this Chapter

Q4.1 Q4.2 Q4.3 Q4.4 Q4.5 Q4.6 Q4.7 Q4.8 Q4.9 Q4.10 Q4.11 Q4.12 Q4.13 Q4.14 Q4.15 Q4.16 Q4.17 Q4.18 Q4.19 Q4.20 Q4.21 Q4.22 Q4.23

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from LAWS OF MOTION
Reference Textbook Solutions
Explore complete chapter exercises for NCERT Physics - Part 1
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring