If the velocity of a car is increased by 20%, then the minimum distance over which it can be stopped increases by (assume uniform acceleration)-

1. 44%
2. 55%
3. 66%
4. 88%

answer is A. how?

To understand how the stopping distance of a car changes when its velocity increases by 20%, we can use the physics of motion, specifically the equations related to uniform acceleration. Let’s break this down step by step.

Basic Concepts of Motion

When a car is moving, it has a certain velocity, and when the brakes are applied, it decelerates until it comes to a stop. The stopping distance can be calculated using the formula:

d = (v² - u²) / (2a)

In this formula:

• d is the stopping distance.
• v is the final velocity (0 m/s when the car stops).
• u is the initial velocity.
• a is the acceleration (which will be negative in this case since it's deceleration).

Initial and Increased Velocity

Let’s denote the initial velocity of the car as u. If the velocity is increased by 20%, the new velocity u' becomes:

u' = u + 0.2u = 1.2u

Calculating Stopping Distances

Now, we can calculate the stopping distance for both the initial and increased velocities. For the initial velocity u, the stopping distance d is:

d = (0 - u²) / (2a) = -u² / (2a)

For the increased velocity u', the stopping distance d' becomes:

d' = (0 - (1.2u)²) / (2a) = -1.44u² / (2a)

Finding the Increase in Stopping Distance

Now, we can express the new stopping distance in terms of the original stopping distance:

d' = 1.44 * (u² / (2a)) = 1.44d

This means that the new stopping distance is 1.44 times the original stopping distance. To find the percentage increase, we can calculate:

Percentage Increase = ((d' - d) / d) * 100

Substituting the values:

Percentage Increase = ((1.44d - d) / d) * 100 = (0.44d / d) * 100 = 44%

Conclusion

Thus, when the velocity of the car is increased by 20%, the minimum distance over which it can be stopped increases by 44%. This illustrates how sensitive stopping distances are to changes in speed, emphasizing the importance of maintaining safe driving speeds.