A car drives with constant velocity of 80km/h on a highway behind a truck (lengt

Question

A car drives with constant velocity of 80km/h on a highway behind a truck (length 25m), keeping a safe distance of 40m. As the driver of the car can see that the lane of the oncoming traffic is free for 300m he starts a passing maneuver, by accelerating with a=1.3m/s2 up to 100km/h.

Does the driver complete the maneuver within the 300m?

How long are the time and the distance it takes to complete the passing maneuver, if a 40m distance is to be kept when getting back into the right lane at the completion of the maneuver?

indepth explaination please...

Explanation / Answer

This is a relative velocity problem

Here the realtive velocity of the car intially is 0 , which accelrates to 20 km/hr or 5.55 m/s in 4.3 secs.

The total time we will have is 300/22.2 = 13.5 secs.

Total length to be covered to pass the truck is = 25+40 m

Intial speed 22.2 m/s and final will be 27.7 m/s. To reach this speed the car will take 4.3 secs

We know that

S = Ut + 0.5 a t^2

S' = V t

Initial relative veloctity is 0

S = 0.5 * 1.3 * 4.3*4.3 = 12m

S' = 5.5 * (13.5 - 4.3) = 50.6 m

THe car won't be able to pass the truck as it iwll just travel 62.6 m in that period.

For the next condition the total distance will be 25 +80 = 105 m

S' = 105 - S = 105 -12 = 93m

t = 4.3 + 93/5.55 = 21 secs

And the distance will be

S = 22.22* 4.3 + 0.5 * 1.3 *4.3*4.3 = 107.5 m

S' = 16.7 *27.77 = 463.7 m

Hence net distance will be = 571.3 m

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