Question

The driver of a 2.0 x 103 kg red car traveling on the highway at 45m/s slams on his brakes to avoid striking a second yellow car in front of him, which had come to rest because of blocking ahead as shown in above Fig. After the brakes are applied, a constant friction force of 7.5 * 10% N acts on the car. Ignore air resistance. (a) Determine the least distance should the brakes be applied to avoid a collision with the other vehicle? (b) If the distance between the vehicles is initially only 40.0 m, at what speed would the collision occur? (C) Write your conclusive observations on the result obtained from this numerical. i.e. the importance of Physics in daily life. ​

Answer 1

Answer:

I found this answer hope it helps

(i)KE=F×S

KE=½mv²

7.5×10³×S=½2.0×10³×45×45

S=270m

(ii) 7.5×10³×40=½2.0×10³v²

v=√300

v=10√3m/s or 17.321m/s

Step-by-step explanation:

Answer 2

Given:

Mass of the red car = 2 X 10³ kg

Velocity of the red car = 45 m/s

Friction force applied = 7.5 × 10³ N

To Find:

(a) The least distance should at which the brakes be applied to avoid a collision with the other vehicle.

(b) The speed of the collision if the distance between the vehicles is initially only 40.0 m.

(c) Conclusive observations

Solution:

(a) Let the least distance be d

We know that Frictional force = μ.N = μmg

This frictional force should be equal to the m.a where a is the acceleration of the car due to the breaks

⇒  ma = μmg

or 2 X 10³ a = -7.5 × 10³

or a =  -3.75 m / s²   (negative because the car is deaccelerating)

Since the acceleration is constant, the stopping distance d can be calculated using the 3rd equation of motion:

$v^2 - u^2 = 2ad$

Taking the final velocity as 0m/s and substituting the values,

45² = 2 X 3.75 X d

or d = 45² / 23.75

or d = 270m

Thus the minimum distance that the two vehicles must separate to avoid a collision is 270m.

b) The speed of collision (v) = $\sqrt{u^2 + 2as}$

or v = $\sqrt{45^2 + 2X3.75X40}$

= $\sqrt{1725}$

=41.53 m/s

Hence the colliding velocity will be 41.53m/s.

c) We can conclude that Newton's laws and equation of motion play a key role in our day-to-day life. The roads and motors are designed through guidelines and rules of physics. The concepts of kinematics also showed us the equations also helped in calculating the safe distance and thus avoiding accidents on the roads.