A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt² – ct³, where b = 2.70 m/s² and c = 0.120 m/s³. Part a Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. Part b Calculate the instantaneous velocity of the car at t = 0.

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt² – ct³, where b = 2.70 m/s² and c = 0.120 m/s³. Part a Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. Part b Calculate the instantaneous velocity of the car at t = 0.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 38P

See similar textbooks

Similar questions

A motorist drives along a straight road at a constant speed of 15.0 m/s. Just as she passes a parked motorcycle police officer, the officer starts to accelerate at 2.00 m/s2 to overtake her. Assuming that the officer maintains this acceleration, (a) determine the time interval required for the police officer to reach the motorist. Find (b) the speed and (c) the total displacement of the officer as he overtakes the motorist.
A speedboat travels in a straight line and increases in speed uniformly from i = 20.0 m/s to f = 30.0 m/s in displacement x of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of i, f, and x. (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
An object moves with constant acceleration 4.00 m/s2 and over a lime interval reaches a final velocity of 12.0 m/s. (a) If its initial velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its initial velocity is -6.00 m/s, what is its displacement during points, (d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations? (e) Explain physically why it does or does not agree.
Dragsters can actually reach a top speed of 145 m/s in only 4.45 s—considerably less time than given in Example 2.10 and Example 2.11. (a) Calculate the average acceleration for such a dragster. (b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for 402 m (a quarter mile) without using any information on time. (c) Why is the final velocity greater than that used to find the average acceleration? Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity.
Physics Review A hockey player strikes a puck, giving it an initial velocity of 10.0 m/s in the positive x-direction. The puck slows uniformly to 6.00 m/s when it has traveled 40.0 m. (a) What is the pucks acceleration? (b) At what velocity is it traveling after 2.00 s? (c) How long does it take to travel 40.0 m? (See Section 2.5.)
Problem 1: Two trucks both cover a straight distance, d = 297 m, in time t = 11.5 s. Truck A moves at a constant velocity (vA). Truck B moves at a constant acceleration (aB), starting from an initial velocity of v0B = 5.9 m/s. Assume both trucks are moving in the positive x-direction. Part (b) What is the final velocity of Truck B? Part (c) What is the acceleration of Truck B?
A car, moving to the left in a straight line in the negative x-direction, travels a distance d = 32 m during time interval Δt = 18 s. In this case, must there be an instant at which the speed of the car is equal to its average speed? Explain answer.
In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, with a maximum speed of 183.58 mi/h. The one‐way course was 5.00 mi long. Acceleration rates are often described by the time it takes to reach 60.0 mi/h from rest. If this time was 4.00 s, and Burt accelerated at this rate until he reached his maximum speed, a. how long did it take Burt to complete the course? b. Sketch position vs time, velocity vs. time, and acceleration vs. time graphs for the race.
At time t0=0.0s, a car, starting from rest, moves south. It continues moving south, and by time tf =121s, it has covered a distance of d=6689m. Take north as the positive x direction, as indicated in the figure. Part A: What is the car's average speed, in meters per second, during this period? Part B: What is the car's displacement, in meters, during this period? Part C: What is the car's average velocity, in meters per second, during this period? Part D: A different car, after starting from rest at t0 =0.0s, travels for the same period, tf =121s, attaining a final velocity of vf =−30.0m/s. What is this car's average acceleration, in meters per squared seconds, during the period described?
1: Two trucks both cover a straight distance, d = 297 m, in time t = 11.5 s. Truck A moves at a constant velocity (vA). Truck B moves at a constant acceleration (aB), starting from an initial velocity of v0B = 5.9 m/s. Assume both trucks are moving in the positive x-direction. Part (b) What is the final velocity of Truck B?
A student begins at rest and then walks north at a speed of v1=0.65m/s. The student then turns south and walks at a speed of v2=0.28m/s. Take north to be the positive direction. a)What is the student's overall average velocity vavg, in meters per second, for the full trip assuming the student spent equal times at speeds v1 and v2? b) If the student travels in the stated directions for 30.0s30.0s at speed v1 and 20.0s at speed v2, what is the net displacement, in meters, during the trip? c) If it takes the student 1.2s to reach the speed v1, from rest, what is the magnitude, in meters per squared second, of the student’s average acceleration during that time?
It has been claimed that an insect called the froghopper (Philaenus spumarius) is the best jumper in the animal kingdom. This insect can accelerate at 4,000 m/s2 over a distance of 2.0 mm as it straightens its specially designed "jumping legs." Assuming a uniform acceleration, answer the following. (a) What is the velocity of the insect after it has accelerated through this short distance? (Enter the magnitude of the velocity.) (m/s) (b) How long did it take to reach that velocity? (ms) (c) How high would the insect jump if air resistance could be ignored? Note that the actual height obtained is about 0.7 m, so air resistance is important here. (m)