Skip to main content
Ch 02: Motion Along a Straight Line
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Capitolo 2, Problema 7a

A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t)=bt2−ct3x(t)=bt^2-ct^3, where b=2.40b = 2.40 m/s2 and c=0.120c = 0.120 m/s3. Calculate the average velocity of the car for the time interval t=0t = 0 to t=10.0t = 10.0 s.

Guida verificata passo dopo passo
1
Understand the problem: We need to calculate the average velocity of the car over the time interval from t = 0 to t = 10.0 seconds. The position of the car as a function of time is given by the equation x(t) = bt^2 − ct^3, where b = 2.40 m/s^2 and c = 0.120 m/s^3.
Calculate the position of the car at t = 0 seconds: Substitute t = 0 into the equation x(t) = bt^2 − ct^3 to find the initial position x(0). This will help us determine the change in position over the time interval.
Calculate the position of the car at t = 10.0 seconds: Substitute t = 10.0 into the equation x(t) = bt^2 − ct^3 to find the final position x(10). This will give us the position of the car at the end of the time interval.
Determine the change in position: Subtract the initial position x(0) from the final position x(10) to find the total displacement of the car over the time interval.
Calculate the average velocity: Use the formula for average velocity, which is the total displacement divided by the total time interval. The average velocity v_avg is given by v_avg = (x(10) - x(0)) / (10.0 - 0).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. It is a vector quantity that considers the direction of motion. In this problem, it involves calculating the change in position of the car from t = 0 to t = 10 seconds and dividing by the time interval.
Video consigliato:
Percorso guidato
05:44
Solving Constant and Average Velocity Problems

Displacement Function

The displacement function x(t) = bt² − ct³ describes the car's position as a function of time. It is crucial to understand how to evaluate this function at specific time points to determine the car's position at those times. This function involves quadratic and cubic terms, indicating non-linear motion.
Video consigliato:
Percorso guidato
08:30
Intro to Wave Functions

Integration of Motion Equations

Understanding how to integrate motion equations is essential for solving problems involving variable acceleration. The given function x(t) can be differentiated to find velocity and acceleration, but for average velocity, evaluating the function at specific times suffices. This concept helps in understanding the relationship between position, velocity, and acceleration.
Video consigliato:
Percorso guidato
11:43
Finding Moment Of Inertia By Integrating
Pratica correlata
Domanda del libro di testo

Starting from the front door of a ranch house, you walk 60.060.0 m due east to a windmill, turn around, and then slowly walk 40.040.0 m west to a bench, where you sit and watch the sunrise. It takes you 28.028.0 s to walk from the house to the windmill and then 36.036.0 s to walk from the windmill to the bench. For the entire trip from the front door to the bench, what are your (a) average velocity? (b) average speed?

364
views
Domanda del libro di testo

A physics professor leaves her house and walks along the sidewalk toward campus. After 55 min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.102.10. At which of the labeled points is her velocity constant and positive?

1781
views
Domanda del libro di testo

A physics professor leaves her house and walks along the sidewalk toward campus. After 55 min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.102.10. At which of the labeled points is her velocity zero?

1322
views
Domanda del libro di testo

You normally drive on the freeway between San Diego and Los Angeles at an average speed of 105105 km/h (6565 mi/h), and the trip takes 11 h and 5050 min. On a Friday afternoon, however, heavy traffic slows you down and you drive the same distance at an average speed of only 7070 km/h (4343 mi/h). How much longer does the trip take?

4008
views
Domanda del libro di testo

A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t)=bt2−ct3x(t)=bt^2-ct^3, where b=2.40b = 2.40 m/s2 and c=0.120c = 0.120 m/s3. Calculate the instantaneous velocity of the car at t=0t = 0, t=5.0t = 5.0 s, and t=10.0t = 10.0 s.

118
views
1
rank
Domanda del libro di testo

In an experiment, a shearwater (a seabird) was taken from its nest, flown 5150 5150 km away, and released. The bird found its way back to its nest 13.513.5 days after release. If we place the origin at the nest and extend the +x+x–axis to the release point, what was the bird's average velocity in m/s for the return flight?

3471
views
1
rank