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Ch. 4 - Applications of the Derivative
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Not the one you use?Change textbook
All textbooksBriggs 3rd EditionCh. 4 - Applications of the DerivativeProblem 4.9.103
Chapter 4, Problem 4.9.103

A car starting at rest accelerates at 16 ft/s² for 5 seconds on a straight road. How far does it travel during this time?

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Step 1: Identify the given values in the problem. The car starts at rest, so the initial velocity (v₀) is 0 ft/s. The acceleration (a) is 16 ft/s², and the time (t) is 5 seconds.
Step 2: Recall the formula for the distance traveled under constant acceleration: s = v0t + 1 2 at² . Since the initial velocity (v₀) is 0, the formula simplifies to s = 1 2 at² .
Step 3: Substitute the given values into the simplified formula. Replace a with 16 ft/s² and t with 5 seconds.
Step 4: Perform the squaring operation on the time value. Compute t² , which is 5² .
Step 5: Multiply the acceleration value by the squared time, then divide by 2 to find the total distance traveled. The result will give the distance in feet.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this problem, kinematics helps us understand how the car's acceleration affects its distance traveled over time.
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Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it has both magnitude and direction. In this scenario, the car accelerates at 16 ft/s², indicating that its velocity increases by 16 feet per second every second, which is crucial for calculating the distance traveled.
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Distance Formula

The distance traveled by an object under constant acceleration can be calculated using the formula: distance = initial velocity × time + 0.5 × acceleration × time². Since the car starts from rest, the initial velocity is zero, simplifying the calculation. This formula allows us to determine how far the car travels during the 5 seconds of acceleration.
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