Question

You are driving on a highway at 30.0 m/s when a car enters the highway 30.0...

You are driving on a highway at 30.0 m/s when a car enters the highway 30.0 m in front of you

traveling at 10.0 m/s and accelerating at 2.00 m/s2. (a) If you do not break (or change lanes), will you hit

the car? If so, how far will you travel before hitting the car? (b) What acceleration is necessary so that you

don’t get any closer than 6.00 m from the car?

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Answer #1

you will hit the car only if you are able to bridge the 30 m gap, let;s look at the possibility.

Let's assume that you hit the car after t seconds

30 (t) = 30 + 10 (t) + 0.5 ( 2)(t^2)

t^2 -20t + 30 =0

t = (20 +- 16.733)/ 2 = 1.633 seconds

the time calculations shows that you would be hitting car after travelling for almost 1.633 seconds

b)distance= 30 (1.633) = 48.99 m apprx

c) this part implies that car tarvelling ahead of you should have sufficinet accelertion , that during the above calculated time, you must have a gap of 6 m between you and teh car ahead of you

distance travlled by you in 1.633 seconds=

10 (1.633) + 0.5 (a) (1.633)^2 - 30 (1.633) = 6

a= 28.99 m/s^2

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