All about physics...?

Question

pls provide me a solution for this problem...

when the front a 5m long bus traveling at constant speed of 20m/s is 55m away from an intersection, the traffic light turns orange. it will take 3secs before the light turns red. the driver's reaction time is 0.25secs. the bus can accelerate up to 2 meters per second squared or slows down at a maximum rate of 4.3 meters per second squared. the intersection is 22m wide. should the driver step on the brakes or on the gas pedal?

Answer 1

I think the bus can stop in about 50 m. So it could stop safely before reaching the intersection. If the driver accelerates, the bus will require over 3 s to clear the intersection so that is a poor idea. I used basic kinematics equations. Is this your answer?

Answer 2

Given:

Db = 5 m = length of bus

Vc =20 m/s = constant speed of truck

Df =55m = distance of front of truck from the intersection

t = 3 sec = time it will take for traffic light to turn from orange to red.

tr = 0.25 sec = driver's reaction time

a = 2 m/s^2 = acceleration of bus if driver steps on gas pedal

d =  4.3 m/s^2 = deceleration of bus if driver steps on brakes

Di = 22 m = width of intersection

Find:  Should the driver step on the brakes or on the gas

           pedal?

Solution:

If the driver decides to step on the gad pedal, then after 3 sec the bus rear end should have cleared the intersection.

The total distance the bus rear end must travel is...

Db + Df + Di = d

5m + 55m + 22m = 82m = d

distance traveled during reaction time(Dr) + distance traveled while bus is accelerating(Da) = D

Dr + Da = D

(Vc)(tr) + (Vc)(3-tr) + (1/2)(a)(3-tr)^2

(20m/s)(0.25sec) + (20m/s)(3.0sec-0.25sec) + (1/2)(2m/s^2)(3.0 sec - 0.25sec)^2

= 67.56 m

Since D<d, then stepping on the gas pedal will not be safe since the rear portion of the bus has not cleared the intersection after 3 sec.

If the driver decides to step on the brakes, the FRONT of the bus must travel a distance of Df = 55m in 3 seconds.  Solving:

(20m/s)(0.25s) + (20m/s)(2.75s)+(1/2)(-4.3m/s^2)(2.75s)^2

= 43.74 m

Since 43.74m<55m, then it is SAFE to steps on the brakes.

Hope this helps.

teddy boy