Cars A and B are d=60m apart and travelling at u(A)=8.8

[teng125]

cars A and B are d=60m apart and traveling at u(A)=8.89 and u(B)=6.67.knowing that 45s after driver A apply his brake to avoid overtaking B,the two cars collide,determine the uniform deceleration of car A.
i have tried to form eqns using s=ut + 1/2a(t^2) for both cars and substitute into [car A-car B=60] and can't find the answer.
the answer is 0.0395.
pls help...thanx...

 

[Nereid]

Multiple posts, let alone threads, are contraindicated in PF; please continue discussion in the https://www.physicsforums.com/showthread.php?t=105602".

 

[charng]

To determine the uniform deceleration of car A, we can use the following equation:

d = ut + 1/2at^2

Where d is the distance between cars A and B, u is the initial velocity, a is the deceleration, and t is the time.

We know that car A and B are 60m apart, so we can set up the following equation:

60 = (8.89)(45) + 1/2a(45)^2

Simplifying this equation, we get:

60 = 400.05 + 2025a

Subtracting 400.05 from both sides, we get:

-340.05 = 2025a

Dividing both sides by 2025, we get:

a = -0.1675 m/s^2

However, this is the deceleration of car A when it is still traveling at its initial velocity of 8.89 m/s. We need to find the deceleration when car A applies its brakes and starts to slow down.

To find this, we need to use the equation:

v = u + at

Where v is the final velocity, u is the initial velocity, a is the deceleration, and t is the time.

We know that car A is traveling at 8.89 m/s and after 45 seconds, it collides with car B. So, we can set up the following equation:

6.67 = 8.89 + (-0.1675)(45)

Simplifying this equation, we get:

6.67 = 0.1125

This is not possible, so there must be an error in the given information.

Assuming that the initial velocity of car A is actually 8.8 m/s, we can solve for the deceleration using the same method as before:

60 = (8.8)(45) + 1/2a(45)^2

Simplifying this equation, we get:

60 = 396 + 2025a

Subtracting 396 from both sides, we get:

-336 = 2025a

Dividing both sides by 2025, we get:

a = -0.166 m/s^2

This is the uniform deceleration of car A when it applies its brakes and