1. Given that the position of a particle is defined in terms of time by the equation below, where x is in meters and t is in seconds, determine: x = t 4t3 +t2 3t2 + 4 t3 (a) the average velocity of the particle from t = 1.0 s to t = 3.0 s, (Ans: vape = 16 m/s) (b) the instantaneous velocity of the particle at t = 2.5 s, (Ans: v, = 20.52 m/s) (c) the average acceleration of the particle from t = 2.0 s to t = 3.0 s, and (Ans: aave = 8.42 m/s?) (d) the t at which the instantaneous acceleration of the particle is 8.10 m/s. (Ans: t = 3.91 s)

1. Given that the position of a particle is defined in terms of time by the equation below, where x is in meters and t is in seconds, determine: x = t 4t3 +t2 3t2 + 4 t3 (a) the average velocity of the particle from t = 1.0 s to t = 3.0 s, (Ans: vape = 16 m/s) (b) the instantaneous velocity of the particle at t = 2.5 s, (Ans: v, = 20.52 m/s) (c) the average acceleration of the particle from t = 2.0 s to t = 3.0 s, and (Ans: aave = 8.42 m/s?) (d) the t at which the instantaneous acceleration of the particle is 8.10 m/s. (Ans: t = 3.91 s)

Name: 1. Given that the position of a particle is defined in terms of time
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: 1. Given that the position of a particle is defined in terms of time by the equation below,where x is in meters and t is in seconds, determine:x =t4t3 +t2 3t2+ 4t3(a) the average velocity of the particle from t = 1.0 s to t = 3.0 s, (Ans: vape = 16

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 2P

See similar textbooks

Similar questions

A race car moves such that, its position fits the relationship x = (5.0 m/s)t + (0.75 m/s3)t3 where x is measured in meters and t in seconds. (a) Plot a graph of the car's position versus time. (b) Determine the instantaneous velocity of the car at t = 4.0 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (c) Compare the average velocity during the first 4.0 s with the results of part (b).
Using approximate values, calculate the slope of the curve in Figure 2.62 to verify that the velocity at t=30.0 s is 0.238 m/s. Assume all values are known to 3 significant figures.
A blue car of length 4.52 m is moving north on a roadway (hat intersects another perpendicular roadway (Fig. P2.81, page 58). The width of the intersection from near edge to far edge is 28.0 m. The blue car has a constant acceleration of magnitude 2.10 m/s2 directed south. The time interval required for the nose of the blue car to move from the near (south) edge of the intersection to the north edge of the intersection is 3.10 s. (a) How far is the nose of the blue car from the south edge of the intersection when it stops? (b) For what time interval is any part of the blue car within the boundaries of the intersection? (c) A red car is at rest on the perpendicular intersecting roadway. As the nose of the blue car enters the intersection, the red car starts from rest and accelerates east at 5.60 m/s2. What is the minimum distance from the near (west) edge of the intersection at which the nose of the red car can begin its motion if it is to enter the intersection alter the blue car has entirely left the intersection? (d) II the red car begins its motion at the position given by the answer to pan (c), with what speed does it enter the intersection?
A glider on an air track carries a flag of length through a stationary photogate, which measures the time interval td during which the flag blocks a beam of infrared light passing across the photogate. The ratio vd = /td is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration, (a) Is vd necessarily equal to the instantaneous velocity of the glider when it is halfway through the photogate in space? Explain. (b) Is vd equal to the instantaneous velocity of the glider when it is halfway through the photogate in time? Explain.
A truck tractor pulls two trailers, one behind the other, at a constant speed of 1.00 102 km/h. It takes 0.600 s for the big rig to completely pass onto a bridge 4.00 102 m long. For what duration of time is all or part of the truck-trailer combination on the bridge?
3 -The speed of an object moving with constant acceleration increases to 12m/s in 6m/s in 3s. What is the acceleration of the object? A) 6 m/^2 B) 4 m/^2 C) 9 m/^2 D) 1 m/^2 E) 2 m/^2
1) What is the displacement of an object dropped from a height after 1.50 seconds? 2) How long will it take a dropped object to reach the ground if dropped from a height of 1.75 meters? 3) An object is flipped upward at a velocity of 30.0 m/s. At what point in its ascent will its velocity be 2.0 m/s? 4) How long will a coin launched upward at a velocity of 25.0 m/s attain a velocity of 15.0 m/s? 5) A 5-kg rock is dropped from a height of 15.0 m. a) What will be its velocity 0.75 seconds after its drop? b) What will be its velocity at a point 8.0 m from the ground? 6) How high will an object launched upward travel if its initial velocity was 15.0 m/s?
1- A particle moves along the x-axis according to the equation x = 2 + 3t - t^2, where x is in meters and t is seconds. Find the position of the particle at t = 3 s. A) 2,4 m B) 3 m C) 2 m D) -2 m E) - 3,2 m
1) If the displacement of a particle is decreasing at a constant rate its velocity is constant. True or False 2) Knowing the position and velocity of a particle allows its future position to be predicted even if its acceleration is unknown. True or False 3) Average acceleration and instantaneous acceleration are always the same. True or False 4) Instantaneous velocity is the derivative of the displacement time function. True or False 5) The slope of the velocity-time graph is the instantaneous acceleration. True or False
The position of a particle moving along the axis given in centimeters by x=9.75+1.75t3,where t is in seconds. A)Calculate the average velocity during the time interval t=2s to t=3s B)Calculate the instantaneous velocity at t=2s C)Calculate the instantaneous velocity at t=3s D) Calculate the instantaneous velocity at t=2.5s E)Calculate the instantaneous velocity when the particle is midway between its positions at t=2s and t=3s
28. A runner moving at a velocity of 6 m/s increases the velocity in a 2 s time interval to a rate of 10 m/s. What is the rate of acceleration? a. 4 m/s^2 b. -4 m/s^2 c. -2m/s^2 d. 2 m/s^2 Explanation and solution
1) The equation of motion of a particle is s = t3 − 3t, where s is in meters and t is in seconds. (Assume t ≥ 0.) (a) Find the velocity and acceleration as functions of t.v(t) = a(t) = (b) Find the acceleration after 5 s.(c) Find the acceleration when the velocity is 0.