Question

In: Physics

Two cars start from rest at a red stop light. When the light turns green, both...

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.4 m/s2 for 4.1 seconds. It then continues at a constant speed for 14.7 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 258.93 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop.

1) How fast is the blue car going 2.5 seconds after it starts?

2)How fast is the blue car going 9 seconds after it starts?

3)How far does the blue car travel before its brakes are applied to slow down?

4)What is the acceleration of the blue car once the brakes are applied?

5) What is the total time the blue car is moving?

6)What is the acceleration of the yellow car?

Solutions

Expert Solution

Here we have given,

The blue car accelerates uniformly at a rate of

a1 = 3.4 m/s2

t1 = 4.1 seconds

t2 = 14.7 seconds,

d2 = 258.93 meters

1. a = (v - u) /t
3.4 = (v - 0)/2.5 s
  v = 8.5 m/s
After 2.5 seconds, the speed of the blue car 8.5 is m/s.

2. After 9 seconds, the blue car is now in the second segment of the motion at constant velocity. Thus,

a = (v - u)/t
3.4 = (v - 0)/4.1 s
V = (13.94) m/s

3. Here total distance = d1 + d2 + d3
d1 = d = u*t + 1/2*at²
d2 = constant velocity*time
  
Total distance =  0*(4.5) + 1/2*(3.4)(4.1)² + (13.94)(14.7) + d3= 258.93
S = d3 = 25.435 m

4.
2aS = v² - u²
2a3(25.435) = 0² - 13.94²
  a3 = -(3.82000393159) m/s²

5. Now Total time will be = t1 + t2 + t3

a3 = (v3 - v2)/t3
-3.8200 = (0 - 13.94)/t3
t3 = (3.64921465969) s

Total time = 4.1 + 14.7 + 3.6492 = 22.4492 s

6. As given here the yellow car just caught up to the blue car in time, the total time would also be 22.4492 s.

d = u*t + 1/2*at²
258.93= 0*t + 1/2*a*(22.4492)²
a = (1.02756813625) m/s²

Which is our required answer.

genius_generous answered 2 years ago
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