QPage 48-49: Q13: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q13 Solution: The increase in the speed of a car is proportional to the…
Students often incorrectly equate acceleration solely with an increase in speed, ignoring that acceleration is any change in the velocity vector. To avoid this, remember that a change in direction (such as uniform circular motion) constitutes acceleration even if the speed magnitude remains constant.
The increase in the speed of a car is proportional to the additional petrol put into the engine. Is it possible to accelerate a car without .....
Step-by-Step Verified Solution
The short, direct answer is:
Yes, absolutely! You can accelerate a car without putting more petrol (or less petrol) into the engine. In fact, you can accelerate a car while keeping the petrol supply constant.
Here is exactly how, broken down step-by-step.
Step 1: What does the question actually state?
The question says:
"The increase in the speed of a car is proportional to the additional petrol put into the engine."
This statement is only about increasing speed (magnitude). In physics, that is called speeding up (positive tangential acceleration). To increase speed, you do need to put more petrol into the engine to generate extra forward force.
But the question asks:
"Is it possible to accelerate a car without putting more petrol or less petrol into the engine?"
In physics, acceleration means any change in velocity—which includes:
- Changing speed (speeding up or slowing down)
- Changing direction (turning)
- Or both
So we are not limited to just speeding up.
Step 2: Case 1 – Turning at constant speed (No change in petrol)
- A car moves at a constant speed on a circular track or a curved road.
- The driver keeps the petrol supply steady (engine force balances friction and air resistance, so speed remains constant).
- Even though the speed is constant, the direction of the car is continuously changing.
- Since velocity (a vector) is changing (direction is changing), the car is accelerating (centripetal acceleration).
- No additional petrol is needed to maintain the turn (friction provides the centripetal force).
✅ So, without putting more or less petrol, the car accelerates by changing direction.
Step 3: Case 2 – Slowing down (Less petrol, but question allows "or less")
The question says "without putting more petrol or less petrol" — meaning exactly the same amount of petrol. But even if we do put less petrol, the car slows down (decelerates), which is also acceleration (negative acceleration).
But since the question forbids "less petrol" as well, let's stick to the constant petrol case above.
Step 4: Case 3 – Driving on an incline (Constant petrol, speed changes!)
- A car is driven up a hill with a constant petrol supply (engine force is constant).
- On an incline, the component of gravity acts against the motion.
- Even with the same petrol, the car may slow down (if gravity's component is greater than engine force).
- On a downhill slope, with the same petrol, the car may speed up (gravity adds to the motion).
- In both cases, the speed changes without changing the petrol input—the change happens because of external forces (gravity).
✅ So, without putting more or less petrol, the car accelerates (speeds up or slows down) simply due to gravity on a slope.
Step 5: Case 4 – Releasing the accelerator pedal (Less petrol – but note)
If you take your foot off the accelerator, you put less petrol, and the car decelerates due to friction and air resistance. That is acceleration (negative). But again, the question specifically asks for without putting more or less — so we focus on the turning and incline cases.
Step 6: Case 5 – Constant petrol, but changing road surface
- With the same petrol supply, if the car moves from a smooth road to a rough road, friction increases, and the car slows down (negative acceleration).
- If it moves from rough to smooth, it speeds up (positive acceleration).
- No change in petrol—just a change in external conditions.
✅ So, acceleration happens without changing petrol.
Quick Summary Table
Situation | Petrol input | Speed | Direction | Acceleration? |
Car turning at constant speed on a curve | Constant | Constant | Changes | ✅ Yes (centripetal) |
Car going uphill with constant petrol | Constant | Decreases | Same | ✅ Yes (negative acceleration) |
Car going downhill with constant petrol | Constant | Increases | Same | ✅ Yes (positive acceleration) |
Car moving from smooth to rough road (constant petrol) | Constant | Decreases | Same | ✅ Yes (negative) |
Car speeding up in a straight line | More petrol | Increases | Same | ✅ Yes, but requires more petrol |
The Core Physics Principle
Acceleration is not just about speeding up. It is any change in velocity.
- Changing speed (with constant petrol) can happen due to external forces like gravity or friction.
- Changing direction (with constant petrol) happens due to centripetal force (from friction or steering).
So you can absolutely accelerate a car without putting more or less petrol into the engine.
Final Answer
Yes, it is possible to accelerate a car without putting more petrol or less petrol into the engine.
The clearest example is taking a turn at constant speed: the car changes direction (so its velocity changes), and therefore it accelerates, even though the petrol supply (and speed) remains constant.
Another example is driving up or down a hill with constant petrol—gravity changes the speed without any change in fuel input.
The key insight is that acceleration is a change in velocity (speed or direction), not just an increase in speed.