Simple but confusing

Two cars emerge side by side from a tunnel. Car A is traveling with a speed of 60 km/h and has an acceleration of 40 km/h/min. Car B has a speed of 40 km/h and an acceleration of 60 km/h/min. Which car is passing the other as they come out of the tunnel? Explain.

Originally posted by clandarkfire
Two cars emerge side by side from a tunnel. Car A is traveling with a speed of 60 km/h and has an acceleration of 40 km/h/min. Car B has a speed of 40 km/h and an acceleration of 60 km/h/min. Which car is passing the other as they come out of the tunnel? Explain.

Car A is passing Car B, however a few moments later Car B will pass Car A.

Explination:

dX_A/dt >dX_B/dt for t < 2 min

dX_A/dt<dX_B/dt for t>2 min

Originally posted by clandarkfire
Two cars emerge side by side from a tunnel. Car A is traveling with a speed of 60 km/h and has an acceleration of 40 km/h/min. Car B has a speed of 40 km/h and an acceleration of 60 km/h/min. Which car is passing the other as they come out of the tunnel? Explain.

Duh, you just SAID they are side by side leaving the tunnel🙂

Yes, but that's not what I'm asking. The tunnel is just there as a frame of reference.

But as far as I can see, Joe Shmo is right.

Next:

A speeding motorist travels past a stationary police officer at a speed of 120km/hr. The officer immediately begins pursuit at a constant acceleration of 10km/hr/s.

a. How long will it take for the police officer to reach the speeder, assuming the speeder maintains a constant speed?

b. How fast will the officer be traveling at that time?

Originally posted by clandarkfire
But as far as I can see, Joe Shmo is right.

Next:

A speeding motorist travels past a stationary police officer at a speed of 120km/hr. The officer immediately begins pursuit at a constant acceleration of 10km/hr/s.

a. How long will it take for the police officer to reach the speeder, assuming the speeder maintains a constant speed?

b. How fast will the officer be traveling at that time?

a. 24 seconds
b. 240 km/h

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sorry something was wrond wit my keyboard

(wrong) (with)

Originally posted by Thomaster
a. 24 seconds
b. 240 km/h

Por qué?

It's probably pretty simple, but I'm just learning how to do this and don't want to come across as stupid.

Originally posted by clandarkfire
Por qué?

It's probably pretty simple, but I'm just learning how to do this and don't want to come across as stupid.

It's useful to know the formula:

Distance travelled = start_distance + start_speed*time + 0.5*acceleration*time**2

At the point of interception the Police officer and the motorist must have travelled the same distance.

For the police officer I used s = 1/2 at², and for the other one I used s = v t.
a = 10 km/h/s
v = 120 km/h
s = s

1/2 × 10t² = 120t
5t² - 120t = 0
5t × (t - 24) = 0
t = 0 or t = 24

In 24 seconds, the police officer drives at 10 × 24 = 240 km/h

Note:
s = 1/2 at²
v = at = s'
a = v' = s''

Originally posted by clandarkfire
Two cars emerge side by side from a tunnel. Car A is traveling with a speed of 60 km/h and has an acceleration of 40 km/h/min. Car B has a speed of 40 km/h and an acceleration of 60 km/h/min. Which car is passing the other as they come out of the tunnel? Explain.

Regardless of their accelerations the current fastest car will pull ahead.

Are we doing your maths homework Clandfire?

Originally posted by iamatiger
Are we doing your maths homework Clandfire?

Hi, I'm Kareem. I'm 16.

Yup.