Math  /  Calculus

QuestionWhich of the following are true?
1. If velocity is constant and positive, then distance traveled during a time interval is the velocity multiplied by the length of the interval.
2. If velocity is positive and increasing, using the velocity at the beginning of each subinterval in a rectangle sum gives an overestimate of the distance traveled. Just 2 Both 1 and 2 Just 1 Neither 1 or 2 Clear my selection

Studdy Solution

STEP 1

1. Velocity is a function of time.
2. The distance traveled can be calculated using the velocity function.
3. We are considering the properties of constant and increasing velocity.

STEP 2

1. Analyze statement 1 regarding constant velocity.
2. Analyze statement 2 regarding increasing velocity.
3. Determine the truth value of each statement.

STEP 3

Statement 1 claims that if velocity is constant and positive, then the distance traveled is the product of velocity and time interval length.
For constant velocity v v , the distance d d traveled over a time interval Δt \Delta t is given by d=v×Δt d = v \times \Delta t .

STEP 4

Statement 2 claims that if velocity is positive and increasing, using the velocity at the beginning of each subinterval in a rectangle sum gives an overestimate.
For increasing velocity, using the initial velocity of each subinterval for a rectangle sum underestimates the area under the curve, not overestimates, because the velocity increases over each subinterval.

STEP 5

Based on the analysis: - Statement 1 is true. - Statement 2 is false.
The correct answer is "Just 1".
The answer is:
Just 1 \text{Just 1}

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