Skip to main content
Pearson+ LogoPearson+ Logo
Ch 02: Motion Along a Straight Line
Back
Previous problem
Next problem
All textbooksYoung & Freedman Calc 14th EditionCh 02: Motion Along a Straight LineProblem 2

Chapter 2, Problem 2

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 − ct3, where b = 2.40 m/s2 and c = 0.120 m/s3. (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s.

Verified Solution
Video duration:
2m
This video solution was recommended by our tutors as helpful for the problem above.
1910
views
Was this helpful?

Video transcript

Welcome back everybody. We have an ambulance whose position with respect to time is given by this equation here where B is 3.1 and C is .147. So I'm gonna go ahead and plug those in that we get that. The position with respect to time is equal to 3.10 times t squared minus 0. t cubed. And we are asked to find the average velocity over this interval of time. Well, the formula for average velocity is given by our change in position over our change in time. Well, our change in time is going to be seven seconds minus zero seconds. So that's just gonna be seven on the bottom. But we still need our change in position or our final position minus our initial position. Let's go ahead and find that by plugging in our different values of T. X evaluated at zero seconds is going to be 3.10. I'm zero squared minus 0. times zero. Cute course this is just zero. Now x evaluated at seven, It's equal to 3.10. I'm seven squared -0.147. I'm seven cubed. Which when you plug into your calculator you get 10, Now that we have. Initial and final position, let's go ahead and plug it into this formula right here. Just once more as a reminder, our average velocity ancient X. Or changing t Equal 10, 1.479 0 over seven. Which when you plug into your clock calculator, you get 14. m/s, which corresponds to our answer choice B. Thank you guys so much for watching. Hope this video helped, and we will see you all in the next one.
Previous problemNext problem
Related Practice
Textbook Question
A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (a) At what time after being ejected is the boulder moving at 20.0 m/s upward?
943
views
Textbook Question
In an experiment, a shearwater (a seabird) was taken from its nest, flown 5150 km away, and released. The bird found its way back to its nest 13.5 days after release. If we place the origin at the nest and extend the +x–axis to the release point, what was the bird's average velocity in m/s (a) for the return flight
1501
views
Textbook Question
You normally drive on the freeway between San Diego and Los Angeles at an average speed of 105 km/h (65 mi/h), and the trip takes 1 h and 50 min. On a Friday afternoon, however, heavy traffic slows you down and you drive the same distance at an average speed of only 70 km/h(43 mi/h). How much longer does the trip take?
2288
views
Textbook Question
A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car's motion, the eastward component of the car's velocity is given by vx(t) = (0.860 m/s^3)t^2. What is the acceleration of the car when vx = 12.0 m/s?
2644
views
2
rank
Textbook Question
CALC. A car's velocity as a function of time is given by v_x(t) = α + βt^2, where α = 3.00 m/s and β = 0.100 m/s^3. (a) Calculate the average acceleration for the time interval t = 0 to t = 5.00 s.
1931
views
1
rank