Question

It is found experimentally that, if a street surface is dry, a good driver can

safely decelerate an automobile with reasonably good tires at the rate of about
4.57 m/s2. So, for a car moving at 60 km/h what should be the minimum
distance between two cars so that they won’t crash during a sudden stop

Answer 1

The minimum distance between two cars so that they won't crash during a sudden stop is approximately 23.7 meters.

Step-by-step explanation:

To find the minimum distance between two cars so that they won't crash during a sudden stop, we need to consider the deceleration of the moving car.

Given that a good driver can safely decelerate an automobile with reasonably good tires at a rate of 4.57 m/s2, and the car is moving at 60 km/h, which is equivalent to 16.7 m/s, we can use the equation of motion:

vf2 = vi2 - 2aΔx

Where vf is the final velocity, vi is the initial velocity, a is the acceleration, and Δx is the distance.

Substituting the given values, we can solve for Δx:

0 = (16.7)2 - 2(4.57)Δx

By rearranging the equation, we find that the minimum distance between the two cars should be approximately 23.7 meters.

Answer 2

Answer: 30.4m

Explanation: vi = 60km/h = 16.67 m/s

a = -4.57m/s^2

vf = 0 m/s

s = ?

`v^(2) _(f) - v^(2) _(i) = 2as \\s = (v^(2) _(f) - v^(2) _(i))/(2a) = ((0m/s)^(2) - (16.67m/s)^(2) )/(2*(-4.57m/s^(2) )) = 30.4 m`