What is the required speed for the last 2 laps to qualify for the race?

In summary, a race car driver needs to average 180 km/h for 4 laps to qualify for a race. Despite only averaging 150 km/h for the first 2 laps due to engine trouble, the driver must maintain a speed of 225 km/h for the last 2 laps in order to reach the required average. This is because the average speed for the entire 4 laps is calculated by dividing the total distance by the total time, and the driver must make up for the slower speed in the first 2 laps by going faster in the last 2 laps. Simply averaging 30 km/h over the required speed for the last 2 laps would not be enough to meet the overall average.
  • #1
Jimbo57
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Homework Statement


"A race car driver must average 180 km/h for 4 laps to qualify for a race. Because of engine trouble, the car averages only 150 km/h over the first 2 laps. What speed must be maintained for the last 2 laps?"


Homework Equations





The Attempt at a Solution


So I do know the answer to be 225km/h but I don't quite understand why. Since half the time trial is completed with the driver being 30km/h below the needed average, wouldn't the 2nd half just be 30km/h above the needed average (210km/h for the last 2 laps)? I'm missing something here.
 
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  • #2
You r averaging the speed for individual laps.. (150 + v)/2 = 180, and thus v=210

Actually avg. speed = total distance/total time = (150*2d + v*2d)/[2d/150 + 2d/v] = 180

In short you r assuming that he takes equal time to complete the first 2 laps and the last 2 laps, which is incorrect.
 

What is one dimensional kinematics?

One dimensional kinematics is the study of motion in a straight line. It involves analyzing the position, velocity, and acceleration of an object as it moves along a single direction.

What are the basic equations used in one dimensional kinematics?

The basic equations used in one dimensional kinematics are the equations of motion:

  • Position: x = x0 + v0t + 1/2at^2
  • Velocity: v = v0 + at
  • Acceleration: a = (vf - v0)/t

What is the difference between speed and velocity?

Speed is a scalar quantity that refers to how fast an object is moving without specifying its direction. Velocity, on the other hand, is a vector quantity that includes both speed and direction. This means that an object can have the same speed but different velocities if it is moving in different directions.

How does acceleration affect an object's motion in one dimension?

Acceleration is the rate of change of an object's velocity. If an object has a positive acceleration, it will speed up in the direction of its motion. If it has a negative acceleration, it will slow down in the direction of its motion. If the acceleration is zero, the object will continue to move at a constant velocity.

What are some real-life examples of one dimensional kinematics?

Some real-life examples of one dimensional kinematics include a car driving along a straight road, a ball being thrown straight up and falling back down, and a person walking in a straight line. These all involve motion in a single direction and can be analyzed using the equations of one dimensional kinematics.

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