10. An object with an initial velocity of 1 m/s to the right is initially at x = 2 m. The objecť's acceleration is a = 2t³. a) Find an expression for the velocity of the object as a function of time, i.e. v(t). b) Find the position of the object as a function of time, i.e. x(t). c) What is the objecť's average velocity and average acceleration between t =1 and t=2 seconds?

10. An object with an initial velocity of 1 m/s to the right is initially at x = 2 m. The objecť's acceleration is a = 2t³. a) Find an expression for the velocity of the object as a function of time, i.e. v(t). b) Find the position of the object as a function of time, i.e. x(t). c) What is the objecť's average velocity and average acceleration between t =1 and t=2 seconds?

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: 1. The position of a particle is given by 7(t) = (2t + 4)î + (-3t² + 5t + 1)ĵ + 6k, where it is…

Q: 1) The light rail train starts from rest and speeds up at a rate of 1.70 m/s² for 13.0 seconds. It…

A: Step 1:Given:The initial speed of the train: v0=0m/sThe train accelerates uniformly for Δt1=13.0s…

Q: particle’s velocity along the x-axis is described by v(t) = A t + B t2, where t is in seconds, v is…

Q: A cheetah accelerates from rest to a maximum velocity of 22.0 i m/s in 2.00 seconds, whilst running…

A: Initial velocity (u) = 0 m/s Final velocity (v) = 22 m/s time taken (t) = 2 seconds

Q: 4. A car accelerates on a straight road from rest to 88 km/h in 6.5 s. What is the magnitude of its…

A: Let the initial velocity of the car is u and final velocity is v , and if the avarage acceleration…

Q: 13. When a 1984 Alfa Romeo Spider sports car accelerates in the x-direction at the maximum possible…

Q: 3. An wind-up toy moves along the x-axis, starting at x = 0 at time t = 0. Its velocity as a…

Q: a. A particle is undergoing a uniform rectilinear motion and the displacement as a function of time…

Q: Given that the position x of a particle (in inches) is defined in terms of time t (in seconds) by…

A: Hi, as this problem contains multiple sub-parts, hence the first three sub-parts will be solved for…

Q: 1. A cyclist travels for 12 min along a straight road. During the first 3.0 min of her trip, she…

Q: 1 de 1 A vehicle drives at a constant speed of 215km/h for 42.3 seconds, accelerates by 29.4m/s2 for…

A: "Since you have asked multiple questions, as per instructions to us, we will solve the first…

Q: An 18-year-old runner can complete a 10.0-km course with an average speed of 4.51 m/s. A 50-year-old…

A: Given value--- distance = 10 km speed of 18 year old runner = 4.51 m/s. speed of 50 year old runner…

Q: 3. An object's position as a function of time is given by the following formula: f(t) = {(0.25…

A: As per guidelines only 3 subparts are solved here.

Q: A bug crawls across a large window. The position of the bug is given by to following equation: x(t)…

Q: 9. A ball is dropped from a height y = H> 0 to the ground y = 0. Sketch plots of the position versus…

A: Free fall motion of a body: A body that is released from some height moves only under the effect of…

Q: Starting from a pillar, you run 400 m east (+x direction) at an average speed of 4 m/s, and then run…

Q: b. What is the acceleration between t = 5.00 s and t = 9.00 s? If the acceleration is to…

A: At t=9 sec, v2 = 40 m/s At t=5 sec , v1 = 20 m/s Acceleration = (v2 -v1)/(t2 -t1 )…

Q: 4. A ball is thrown straight up at initial speed of 5 m/s and falls down to the same start point.…

A: Throwing ball straight up is a special case projectile so to solve the given problem all the…

Q: 1. Visualization (a) The middle graph below shows the velocity of a mouse (running back and forth…

A: Given that, the initial position t=0 of the mouse is xo=+3m and the velocity uo=+1m/s From the…

Q: 7. Carl Lewis set a world record for the 100.0-m run with a time of 9.86 s. If, after reaching the…

Q: 2. At time t=0 s, an object is observed at x = 0 m; and its position along the x axis follows this…

Q: A mountain lion is napping in the shade as a deer saunters by at steady 48.2 km/h. Feeling the…

Question

10. An object with an initial velocity of 1 m/s to the right is initially at x = 2 m. The
objecť's acceleration is a = 2t³.
a) Find an expression for the velocity of the object as a function of time, i.e. v(t).
b) Find the position of the object as a function of time, i.e. x(t).
c) What is the objecť's average velocity and average acceleration between t =1 and t=2
seconds?

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

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 5 images

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

One afternoon, a student was going home after attending a calculus class. For this reason, the student orders an online motorcycle taxi through the application. At the time of ordering, the online motorcycle taxi is in the position s = 2t² + 2t+4, where t is in units of time and s is in meters. a. Determine the average speed of the online motorcycle taxi at intervals of 3 minutes to 5 minutes. b. Determine the time when the instantaneous speed of the online motorcycle taxi is exactly the same as the average speed. NEED IN RUSH THANKS
#1
3. A ball is thrown upwards at 13.0 m/s toward the ceiling located 6 m above the point where you release the ball. Air resistance is negligible. Objects falling near the earth's surface with no forces acting except gravity have a downwards acceleration of magnitude g. For this problem use g = 10 m/s². Write any equation you use in symbolic form before substituting in numbers. Make a labeled picture with symbols and all relevant values. Put a coordinate system on the a. picture by indicating the location of the origin and position direction. b. Find the time taken to reach the ceiling. Find the velocity just before the ball touches the ceiling. C.
ates) Tılı 80 1. The following graph displays the position of an object versus time. x(t) (m) 4 ● Accessibility: Investigate 2 The acceleration is positive The velocity is negative The speed is +0.5 m/s The position is at a maximum The object is still 900 2 4 Normal tv Using the graph, match each description of motion to the correct time interval. Not all given options are answers. No Spacing H + 6 8 10 Heading 1 MacBook Air t (sec) a) 0 4 e f) only 8 < t < 10 g) t < 2 h) none of the above DII Headine ● X . Fo
3. In Physics, the height of a free-falling object at a given time t is given by h = –16t² + v,t + h., where v, is the initial velocity, and h, is the initial height. A student throws a ball upward from a height of 48ft, initially at 32 ft/s. What is the maximum height of the ball?
1. A particle moves according to the equation x = 2t³ - 2t + 1, where x is in meters and t in seconds. (a) Find instantaneous acceleration as a function of time. (b) Find the value of the instantaneous acceleration at t = 3.5 s.
5. Draw a distance vs. time graph for Melinda’s journey. Her home is located at 0 meters.Melinda is riding her bike over to her friend Sara’s house to complete an assignment. Her friend lives 5 km away. She accelerates away from her home for250 m in the next 2.5 minutes. She then rides at a constant speed of 300 m/min for 15 minutes. Melinda sees Sara’s house approaching so she slows downuntil she reaches her destination in the next 2.5 minutes. She stays at Sara’s house for 30 minutes while they work on the assignment. It is time to go home,Melinda rides home at a steady speed of 250 m/min for 10 minutes. Melinda is getting tired so she slows down for 250 m during the next 5 minutes thenstops for 2.5 minutes to have a drink. Realizing it’s getting late, she had to speed up 1 km in the next 5 minutes then rides at a constant speed of 300 m/minfor 2.5 minutes. Almost home, she decelerates for the next 10 minutes until she reaches her house.
#2
4. A robotic vehicle is exploring the surface of Mars. The robot, which is represented as a point, has x - and y-coordinates that vary with time: x = (3 − 2t); y = (-t² + 4t³) where x and y are in meters and t is in seconds. a. Find the average velocity of the robot between t = 0s and t = 2s. b. Find the average acceleration of the robot between t = 0s and t = 2s. c. At what time the acceleration of the robot will be zero. a. Vavg= -21 + 14ĵ m/s b. davg = 22ĵ C. m s² 2 t = = = 0.083 s 24
4. Marcus throws a rock straight up into the air. It leaves his hand 1.2 meters above the ground, and it hits the ground 3.5 seconds later. Find a. the initial speed of the rock when it leaves his hand b. the maximum height the rock reaches before falling back down, relative to the ground c. the speed of the rock right before it hits the ground
1. The acceleration of a car is given by a(t) = A – Bt + Ct² , where A = 1.0 m/s², B = 0.5 m/s³, C = 2.0 m/s“. The car is at rest at the origin at time t= 0. Find its position and velocity as a function of time. b. Sketch its position, velocity, and acceleration. a.
An object is moving to the right with a constant speed of 21 m/s for 5.0 s. What is the acceleration of the object, in m/s²? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.