How long does it take an automobile?

Question

How long does it take an automobile traveling in the left lane at 50.0 km/h to pull alongside a car traveling in the same direction in the right lane at 30.0 km/h if the cars' front bumpers are initially 80 m apart?

Answer 1

mikelyt78 was almost correct - he converted the speed to meters per minute - failing to take into account the number of seconds in a minute (500 m/s is super fast)

Now for the correct answer:

This question can be greatly simplified by assuming the car in the right lane is stationary, while the car in the left lane is traveling at 20 km/hr (which is the difference in speed between the two vehicles). Now all we have to do is apply the following equation:

(xf - xi) = vi*t + (1/2)*a*t^2

Where:

xf = 80 m
xi = 0 m
vi = 20 km/hr
t = ?
a = 0

Solving for t, the new equation reads:

t = (xf - xi)/vi = (80 m - 0 m)/20 km/hr = .004 hr --> multiply this by 3600 to get your answer in seconds which is = 14.4 s

Answer 2

The differential velocity is 50 - 30, or 20km/h. that is the "cloxing velocity". It has to cover 80m from the formula d = v*t, t = d/v in this case 80/20 sec

Answer 3

gp4rts was almost correct except that you have to convert km to meters and hours to seconds.

50km/h = 50000m/60secs = 833.33m/s
20km/h = 20000m/60sec = 333.33m/s

so 833-333 = 500m/s

divided 80m apart by 500m/s, you'll get 0.16 sec