Two cars A and B are moving in same direction with velocities 30 m/s a

1.	Two cars A and B are moving in same direction with velocities 30 m/s and 20 m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2 m/s2. There will be no collision when d is
Answer» DISTANCE BETWEEN THE CARS TO AVOID COLLISION It's very simple, The Distance between the two cars must be greater than or equal to the distance travelled by the car A after applying the breaks w.r.t carB. Car A :- After applying the break, The final VELOCITY, v will be 0 m/s. because the car would come to rest. Given,Relative Initial velocity of carA w.r.t carB , Initial velocity of carA - Initial velocity of carB ⇒ u' = 30 - 20 ⇒ u' = 10 m/s And uniform acceleration produced as a result of applying the brakes, a = -2 m/s² Using Third equation of MOTION, we get: ⇒ 2as = v² - u² ⇒ 2×-2×s = (0)² - (10)² ⇒ -4s = -100 ⇒ s = 25 m Here, The carA would travel 25m after applying the breaks w.r.t carB. So We CONCLUDE that the carA must be at a distance greater than 25m in order to avoid collision with car B. More EQUATIONS of Motion :- ⇒ v = u + at ⇒ h = ut + 1/2 (at²) Where, v = Final velocity u = Initial velocity a = Acceleration t = TIME taken h = Height

Two cars A and B are moving in same direction with velocities 30 m/s and 20 m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2 m/s2. There will be no collision when d is

Answer»

DISTANCE BETWEEN THE CARS TO AVOID COLLISION

It's very simple, The Distance between the two cars must be greater than or equal to the distance travelled by the car A after applying the breaks w.r.t carB.

Car A :-

After applying the break, The final VELOCITY, v will be 0 m/s. because the car would come to rest.

Given,Relative Initial velocity of carA w.r.t carB , Initial velocity of carA - Initial velocity of carB

⇒ u' = 30 - 20 ⇒ u' = 10 m/s

And uniform acceleration produced as a result of applying the brakes, a = -2 m/s²

Using Third equation of MOTION, we get:

⇒ 2as = v² - u²

⇒ 2×-2×s = (0)² - (10)²

⇒ -4s = -100

⇒ s = 25 m

Here, The carA would travel 25m after applying the breaks w.r.t carB. So We CONCLUDE that the carA must be at a distance greater than 25m in order to avoid collision with car B.

More EQUATIONS of Motion :-

⇒ v = u + at

⇒ h = ut + 1/2 (at²)

Where,

v = Final velocity
u = Initial velocity
a = Acceleration
t = TIME taken
h = Height