Stopping Distance Formula Explained with Solved Examples | Reaction & Braking Distance

 - Dr Sanjay Kumar Pawar

Stopping Distance: Formula, Reaction Distance, Braking Distance & Questions

Stopping Distance consists of Reaction Distance and Braking Distance. Learn the formula with an easy solved example.

Internal Links

• Motion in a Straight Line
• Equations of Motion
• Uniform and Non-Uniform Motion
• Speed, Velocity and Acceleration
• Distance and Displacement
• Newton's Laws of Motion
• Friction in Physics
• Work, Energy and Power
• Projectile Motion
• Free Fall Equations
• Average Speed Formula
• Relative Motion
• SUVAT Equations
• Kinematics Notes
• Physics Formula Sheet

Stopping Distance (Reaction Distance + Braking Distance)

What is Stopping Distance?

When a driver sees an obstacle, the car does not stop immediately. The car travels some distance before stopping completely.

The stopping distance has two parts:

• Reaction Distance → Distance travelled while the driver reacts.
• Braking Distance → Distance travelled after applying the brakes.

Stopping Distance = Reaction Distance + Braking Distance

S = Sr + Sb

1. Reaction Distance

Sr = u × t

Where

• u = Initial speed (m/s)
• t = Reaction time (seconds)

2. Braking Distance

Use the equation of motion:

v² = u² + 2as

When the car stops:

• v = 0
• a = Retardation

Therefore,

Sb = u² / 2a

Solved Example

Question

A car is moving with velocity 20 m/s. The driver's reaction time is 0.5 s. The maximum retardation is 4 m/s². Find the stopping distance.

Step 1 : Reaction Distance

Sr = u × t

Sr = 20 × 0.5

Sr = 10 m

Step 2 : Braking Distance

Sb = u² / 2a

= 20² / (2 × 4)

= 400 / 8

= 50 m

Step 3 : Stopping Distance

S = Sr + Sb

= 10 + 50

= 60 m

Answer = 60 m

Shortcut Formula

Stopping Distance

S = ut + u² / 2a

Important Points

• Reaction distance depends on reaction time.
• Braking distance depends on speed and braking force.
• Higher speed means longer stopping distance.
• Wet roads increase braking distance.
• Always maintain a safe distance while driving.

Practice Questions

Q1. A car moves at 10 m/s. Reaction time = 1 s Retardation = 5 m/s² Find stopping distance.

Q2. A car moves at 30 m/s. Reaction time = 1 s Retardation = 6 m/s² Find stopping distance.

Q3. A car moves at 15 m/s. Reaction time = 0.4 s Retardation = 3 m/s² Find stopping distance.

Q4. A car moves at 25 m/s. Reaction time = 0.8 s Retardation = 5 m/s² Find stopping distance.

Answers

Question	Answer
Q1	20 m
Q2	105 m
Q3	43.5 m
Q4	82.5 m

Quick Revision

Quantity	Formula
Reaction Distance	Sr = ut
Braking Distance	Sb = u² / 2a
Stopping Distance	S = Sr + Sb

Memory Trick

Think → Brake → Stop

• Think = Reaction Distance
• Brake = Braking Distance
• Stop = Stopping Distance

© Physics Notes for Beginners

Stopping Distance, Reaction Distance & Braking Distance Explained | NEET Physics Notes

- Dr Sanjay Kumar Pawar 

Reaction Distance, Braking Distance and Stopping Distance for NEET 

Stopping distance consists of reaction distance and braking distance, an important concept in NEET Physics.

Internal Links

1. Motion in One Dimension Notes
2. Distance, Displacement and Speed
3. Velocity and Acceleration Explained
4. Equations of Motion (SUVAT Equations)
5. Uniform and Non-uniform Motion
6. Graphs of Motion (Distance-Time & Velocity-Time)
7. Relative Motion Notes
8. Newton's Laws of Motion
9. Friction and Braking Force
10. Work, Energy and Power
11. Circular Motion
12. NEET Physics Formula Sheet
13. Top 100 NEET Physics MCQs
14. Kinematics Practice Questions
15. NEET Physics Revision Notes 

Stopping Distance (Reaction Distance + Braking Distance)

Definition

Stopping distance is the total distance travelled by a vehicle from the moment the driver notices an obstacle until the vehicle comes to complete rest.

Stopping Distance = Reaction Distance + Braking Distance

S = sr + sb

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1. Reaction Distance (Thinking Distance)

Reaction distance is the distance travelled by the vehicle during the driver's reaction time before applying the brakes.

Reaction Time

Reaction time is the time taken by the driver from observing an obstacle to applying the brakes.

Generally, Reaction Time < 1 second

Formula

sr = u × tr

Where,

• sr = Reaction Distance
• u = Initial Velocity
• tr = Reaction Time

During reaction time:

• Brakes are not applied.
• Velocity remains constant.
• Acceleration = 0

---

2. Braking Distance

Braking distance is the distance travelled after applying the brakes until the vehicle comes to rest.

During braking,

• Vehicle decelerates.
• Final velocity becomes zero.

Formula

v² = u² − 2as

Since

v = 0

Therefore,

sb = u² / 2a

Where

• sb = Braking Distance
• a = Deceleration

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3. Stopping Distance Formula

S = ut_r + u² / 2a

This is the most important formula for NEET examinations.

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4. Safe Distance

Safe distance is the minimum distance required between two vehicles to avoid collision.

Safe Distance ≥ Stopping Distance

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5. Difference Between Reaction Distance and Braking Distance

Reaction Distance	Braking Distance
Before applying brakes	After applying brakes
Velocity remains constant	Velocity decreases
Acceleration = 0	Negative acceleration
Depends on reaction time	Depends on braking force

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6. Important NEET Points

• Reaction distance depends on speed and reaction time.
• Braking distance depends on speed².
• If speed doubles, braking distance becomes four times.
• Stopping distance = Reaction distance + Braking distance.
• Reaction time is usually less than 1 second.

---

7. Formula Sheet

Reaction Distance = u × tr

Braking Distance = u² / 2a

Stopping Distance = ut_r + u² / 2a

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8. Practice Questions

Q1. A car moves with speed 20 m/s. Reaction time is 0.5 s. Find the reaction distance.

Answer: 20 × 0.5 = 10 m

Q2. A vehicle moves at 30 m/s. Braking deceleration is 5 m/s². Find braking distance.

Answer: 30² / (2 × 5) = 900 /10 = 90 m

Q3. A car travels at 25 m/s. Reaction time = 0.8 s Deceleration = 5 m/s² Find stopping distance.

Reaction Distance = 25 × 0.8 = 20 m
Braking Distance = 25² /10 = 62.5 m
Stopping Distance = 20 + 62.5
= 82.5 m

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9. Multiple Choice Questions

1. During reaction time acceleration is
   • A. Positive
   • B. Negative
   • C. Zero ✔
   • D. Infinite
2. Reaction distance depends upon
   • A. Speed
   • B. Reaction time
   • C. Both A and B ✔
   • D. Braking force
3. Braking distance is proportional to
   • A. Speed
   • B. Speed² ✔
   • C. Time
   • D. Mass only
4. Stopping distance equals
   • A. Reaction distance
   • B. Braking distance
   • C. Reaction distance + Braking distance ✔
   • D. None
5. If speed doubles, braking distance becomes
   • A. Double
   • B. Half
   • C. Four Times ✔
   • D. Eight Times

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10. One Minute Revision

✔ Reaction Distance = Before braking
✔ Braking Distance = After braking
✔ Stopping Distance = Reaction Distance + Braking Distance
✔ Reaction Distance = u × tr
✔ Braking Distance = u² / 2a
✔ Stopping Distance = ut_r + u² / 2a
✔ Braking Distance ∝ Speed²

Prepared for NEET Physics Students

Topic: Reaction Distance • Braking Distance • Stopping Distance