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 1 year ago

Next > < Previous

Related Solutions

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 4.7 m/s2 for 3.8 seconds. It then continues at a constant speed for 8.5 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 206.78 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the...

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 4.7 m/s2 for 3.8 seconds. It then continues at a constant speed for 8.4 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 205 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the...

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...

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 4.7 m/s2 for 3.8 seconds. It then continues at a constant speed for 8.7 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 212 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the...

Design a Traffic Light that upon reset, turns Red for 10 seconds, then Green for 10...

Design a Traffic Light that upon reset, turns Red for 10 seconds, then Green for 10 seconds, then Yellow for 5 seconds. Assume a CLK period of 5 seconds. Draw the State Transition Diagram, State Transition Table and Output Table, find the Boolean Equations for Next State and Output and draw the logic circuit.

In a demolition derby, two cars start from rest at opposite ends of a track. At...

In a demolition derby, two cars start from rest at opposite ends of a track. At exactly the same instant they begin to accelerate towards each other in a straight line. Car A accelerates at a rate of aA = 3.0 m/s2 , while Car B accelerates at a rate of aB = 4.0 m/s2 in the opposite direction. After 6.5 s the cars collide. Please use a coordinate system where Car A is travelling in the positive direction. a)(8...

When the light turns yellow, should you stop or go through it? An article defines the...

When the light turns yellow, should you stop or go through it? An article defines the “indecision zone” as the period when a vehicle is between 2.5 and 5.5 seconds away from an intersection. It presents observations of 750 vehicles passing through various intersections in Vermont for which the light turned yellow in the indecision zone. Of the 750 vehicles, 89 ran a red light. a) Find a 90% confidence interval for the proportion of vehicles that will run the...

When the light turns yellow, should you stop or go through it? An article defines the...

When the light turns yellow, should you stop or go through it? An article defines the “indecision zone” as the period when a vehicle is between 2.5 and 5.5 seconds away from an intersection. It presents observations of 750 vehicles passing through various intersections in Vermont for which the light turned yellow in the indecision zone. Of the 750 vehicles, 89 ran a red light. Find a 90% confidence interval for the proportion of vehicles that will run the red...

In a quarter-mile drag race, two cars start simultaneously from rest, and each accelerates at a...

In a quarter-mile drag race, two cars start simultaneously from rest, and each accelerates at a constant rate until it either reaches its maximum speed or crosses the finish line. Car A has an acceleration of 10.9 m/s2 and a maximum speed of 109 m/s. Car B has an acceleration of 11.8 m/s2 and a maximum speed of 93.7 m/s. (a) Which car wins the race? (b) By how many seconds does this car win the race?

1. Two cars are moving on a road and both start at the same place at...

1. Two cars are moving on a road and both start at the same place at time ?=0. The velocity of car number 1 is given by ?1(?)=sin?+1 and the velocity of car number 2 is given by ?2(?)=cos?+1. a. Which car is ahead at ?=?2 ,?=?,?=3?? [3 marks] b. Write down a definite integral which gives the total distance traveled by car number 1 from ?=0 to ?=10. [3 marks] b. Write down a definite integral which gives the...

Subjects