T = d/r

Definition

The equation t = d/r, where t represents time, d represents distance, and r represents rate or speed, is a fundamental relationship in the context of uniform motion and work applications. This equation allows for the calculation of the time required to cover a certain distance at a given rate or speed.

5 Must Know Facts For Your Next Test

1. The equation t = d/r is used to solve problems involving uniform motion, where an object travels a certain distance at a constant rate or speed.
2. This equation is also applicable in work applications, where the time required to complete a task can be determined based on the distance and rate of work.
3. The variable t represents the time required to cover the distance d at the given rate r.
4. Rearranging the equation, one can also solve for distance (d = r * t) or rate (r = d/t) when the other two variables are known.
5. Understanding the relationship between time, distance, and rate is crucial for solving problems related to uniform motion and work applications.

Review Questions

• Explain how the equation t = d/r is used to solve problems involving uniform motion.
  • In the context of uniform motion, the equation t = d/r is used to determine the time required for an object to travel a certain distance at a constant rate or speed. For example, if a car travels a distance of 100 miles at a rate of 50 miles per hour, the time required to cover that distance can be calculated using the equation t = d/r, which in this case would be t = 100 miles / 50 miles per hour = 2 hours. This relationship is fundamental in solving problems related to uniform motion, where the distance, rate, and time are interconnected.
• Describe how the equation t = d/r can be applied to work applications.
  • The equation t = d/r can also be used in the context of work applications, where the time required to complete a task is determined based on the distance and rate of work. For instance, if a worker needs to move a pile of bricks a distance of 20 meters at a rate of 5 meters per minute, the time required to complete the task can be calculated using the equation t = d/r, which would be t = 20 meters / 5 meters per minute = 4 minutes. This relationship is useful in planning and scheduling work tasks, as well as in understanding the efficiency and productivity of various work processes.
• Analyze the implications of rearranging the equation t = d/r to solve for other variables, such as distance or rate.
  • The equation t = d/r can be rearranged to solve for other variables, such as distance (d = r * t) or rate (r = d/t), when the other two variables are known. This flexibility in the equation allows for a deeper understanding of the relationships between time, distance, and rate. For example, if the time and rate are known, the distance can be calculated by rearranging the equation to d = r * t. Similarly, if the distance and time are known, the rate can be calculated by rearranging the equation to r = d/t. This ability to solve for different variables based on the given information is crucial in a wide range of applications, from transportation and logistics to project management and engineering.

Related terms

Uniform Motion:

Uniform motion refers to the motion of an object at a constant speed, where the distance traveled is directly proportional to the time elapsed.

Work: Work is the product of force and displacement, and it is a measure of the energy expended in moving an object a certain distance.

Rate:

Rate is the measure of change or movement, typically expressed as a quantity per unit of time, such as miles per hour or meters per second.