Suppose the velocity of a car is 10 m/s at t = 0 s, and is 20 m/s at t = 30 s. Which of the following must be true?
The car had a positive instantaneous velocity in the interval.
The car had a positive instantaneous acceleration at each moment in the interval.
The car had a positive average velocity over the interval.
The car had a positive average acceleration over the interval.***************
To determine which of the statements must be true, let's analyze the given information:
- The velocity of the car at t = 0s is 10 m/s, and at t = 30s, it is 20 m/s.
Now let's examine each statement and see if it is true or not:
1. The car had a positive instantaneous velocity in the interval.
Instantaneous velocity refers to the velocity at a specific moment in time. Since the velocity of the car is given as 10 m/s at t = 0s and 20 m/s at t = 30s, we can see that the car's velocity is positive throughout the entire interval. Therefore, this statement is true.
2. The car had a positive instantaneous acceleration at each moment in the interval.
Instantaneous acceleration refers to the rate of change of velocity at a specific moment in time. Since we are not given any information about the car's acceleration at different time points within the interval, we cannot determine whether the car had a positive instantaneous acceleration at each moment. Therefore, this statement cannot be determined from the information given.
3. The car had a positive average velocity over the interval.
Average velocity is the total displacement divided by the total time taken. Since we are not given any information about the total displacement of the car or the time taken over the interval, we cannot determine whether the car had a positive average velocity. Therefore, this statement cannot be determined from the information given.
4. The car had a positive average acceleration over the interval.
Average acceleration is the change in velocity divided by the change in time. In this case, the velocity of the car increased from 10 m/s to 20 m/s over a time interval of 30s. Since the change in velocity is positive and the change in time is positive, the average acceleration would be positive. Therefore, this statement is true.
Based on our analysis, the only statement that must be true is: "The car had a positive average acceleration over the interval."