(1) The position s(t) of an object moving along the x-axis is given by s(t) = 3t¹ - 8t³ - 15t². For this problem s(t) is measured in meters, and t is measured in seconds. (a) What is the average velocity of the object over the interval [0, 2]? (b) (c) What is the instantaneous velocity of the object at t = 2? Find all values of t in the interval [0, 5] when the object is momentarily stopped.

(1) The position s(t) of an object moving along the x-axis is given by s(t) = 3t¹ - 8t³ - 15t². For this problem s(t) is measured in meters, and t is measured in seconds. (a) What is the average velocity of the object over the interval [0, 2]? (b) (c) What is the instantaneous velocity of the object at t = 2? Find all values of t in the interval [0, 5] when the object is momentarily stopped.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: A soccer player kicks a rock horizontally off a 44 m high cliff into a pool of water. If the player…

Q: A particle moves according to a law of motion s = f(t) = t³ - 15t² + 72t, tz 0, where t is measured…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: In this problem “down” is taken to be positive (+), acceleration is “a” and velocity is “v”. An…

A: acceleration due to gravity is 9.8 m/s2 .thus direction of acceleration = positive

Q: A rock thrown straight up into the air has a velocity of y(t) = -9.8t + 20 meters per second after t…

A: Given data The velocity of the rock is yt=-9.8t+20 The duration of the rock is t = 2 s

Q: The position of an object in METERS is given by X(t) = B-t" + C-t %3D Find the Sl units of the…

Q: A model rocket shot straight upward with an initial velocity of vo = 25 m/s will reach a height of h…

A: Given data: Initial velocity of rocket, vo=25 m/s Height, ht=-4.9t2+25t

Q: (b) Determine the acceleration at t = 2.0 s. SOLUTION (Use the following as necessary: t and At.)…

Q: An object's position as a function of time is given by the expression; x(t) = 14.7/(t+1) + 2.9t3 -…

Q: An object moves in a plane from the position r1=(-4,-5) m to the position r2=(-2,6) m and then to…

Q: ball is thrown straight up with an initial velocity of 40 m/s, so that its height (in meters) after…

Q: inate of an objectis given as a function of time by x(t)=7t-3t2, where x in meter and t in seconds.…

A: The coordinate of a system is given by as a function of time as:- xt=7t-3t2 ----(1) [Here x is…

Q: A projectile is fired in the air from a height of 125 feet. Its velocity (in feet per second) t…

A: Given: t (s) 0 5 10 15 20 25 30 f(t) (ft/s) 234 215 196 169 150 120 109

Q: A vehicle accelerates down an on ramp and eventually reaches highway speed. The position of the…

A: The position of the particle at any time is given by the equation: x(t) = At2t +B Now as the…

Q: The acceleration of a particle is defined by the relation a=-kx² where a in m/s², X in meters. the…

Q: A particle moves according to a law of motion s = f(t) = t³ - 15t² + 72t, t≥ 0, where t is measured…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: (a) A soccer player kicks a rock horizontally off a 35 m high cliff into a pool of water. If the…

A: Part-(a): Let's assume upward and rightward as positive direction. Take horizontal direction as…

Q: If an object is shot upward with an initial velocity, v 0, in feet per second (ft/s), the velocity,…

Q: A runner with a good awareness of her pace runs along a path of unknown length at a speed of…

A: We need to find the distance run by the athlete.

Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

Q: An object moves in a plane from position r1=(-1,-2) m to the position r2=(-2,7 m and then to…

Q: A ball dropped from a state of rest at time t = 0 travels a distance s(t) = 4.9t 2 mint seconds.(a)…

A: It is given as,

Q: Suppose a migrating bird flies at a constant altitude of 5 km, with a velocity of 42 km/h. At time t…

Q: An object's (one dimensional) motion is represented by the following graph of position 5) versus…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Concept explainers

Distance and Speed

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –

Question

(1) The position s(t) of an object moving along the x-axis is given by s(t) = 3t¹ – 8t³ .
this problem s(t) is measured in meters, and t is measured in seconds.
(a)
What is the average velocity of the object over the interval [0, 2]?
(b)
(c)
What is the instantaneous velocity of the object at t 2?
15
2
t². For
Find all values of t in the interval [0, 5] when the object is momentarily stopped.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

7:31 a 4 O 0令ll回 10. The displacement of the object between t = 0 and t = 4 s is: (A) 22 m (B) 28 m (C) 40 m (D) 42 m (E) 60 m Velocity (mis) Time (b a e 11. The above graph represents the velocity as a function of time of a moving object. What is the net displacement between t = 0 s and t = 4 s? (A) Om (B) 16 m (C) 24 m (D) 36 m (E) 48 m Acceleration vs Time Time (s) a
The position versus time for a certain particle moving along the x axis is shown in the figure below. Find the average velocity in the following time intervals. х (m) 10 8 4 t (s) 1 2 3 4 5 6 7 8 -2 -4 -6 (a) 0 to 2 S m/s (b) 0 to 3 s m/s (c) 3 to 6 s m/s
A space probe on the surface of Mars sends a radio signal back to the Earth, a distance of 7.96 ✕ 107 km. Radio waves travel at the speed of light (3.00 ✕ 108 m/s). How many seconds does it take for the signal to reach the Earth?
IXFQP A police car traveling 95.0 km/h is traveling west, chasing a motorist traveling at 80.0 km/h. What is the velocity of the motorist relative to the police car? What is the velocity of the police car relative to the motorist? If they are originally 250 m apart, in what time interval will the police car overtake the motorist? (Only the third part appears on the answer sheet.) [S] E08 04.35] 5. A. 53.76 s D. 64.87 s 48.63 s E. 65.66 s 60.00 s F. 74.72 s IXXKI MacBook Pro & 7 2 W ARCH B. C. 1--1 #3 E 54 $ R % 5 T Y U *00 8 ( 9 -O O 0 1 P + {
When a ball is dropped from a state of rest at time t = 0, the distance it has travelled after t seconds is s(t) = 4.9t? meters. (a) How far does the ball travel during the time interval [3, 3.5]? (Use decimal notation.) distance: meters (b) Compute the average velocity over the time interval [3,3.5]. (Use decimal notation.) average velocity: m/sec (c) By computing the average velocity over the time intervals [3,3.1], [3, 3.01], and [3, 3.001], estimate the ball's instantaneous velocity at t = 3. (Round your answer to one decimal place.) instantaneous velocity: m/sec
15 25 30 35 50 60 (sec) v(1) (f/sec) -20 -30 -20 -14 -10 10 a(t) 2 2. 4 (1/sec") A car travels on a straight track. During the time interval 0sts 60 seconds, the car's velocity v, measured in feet per second, and acceleration a, measured in feet per second per second, are continuous functions. The table above shows selected values of these functions. а, For 0
A particle moving along a straight line has initial velocity v(0) = 1 m/s, and acceleration a(t) = sin(I-t) + cos(t+1) (in m/s?). (a. Find the velocity at time t. (b) Find the average velocity during the time interval [I, 211]. (c) Find the distance traveled during the time interval [1, 2I].