Question

Instantaneous Velocity: 1.1. An object moves along a straight path, and its position function is $s(t) = 2t^2 - 3t + 4$. Find the instantaneous velocity of the object at $t = 3$ s. 1.2. A bicycle travels along a road, and its velocity-time graph is a straight line with a slope of $2 \text{ m/s}^2$. Determine the instantaneous velocity of the bicycle at any time. 1.3. A car is initially at rest. Its velocity-time graph shows a constant positive slope of $5 \text{ m/s}^2$. Calculate the instantaneous velocity after 4 s. 1.4. Describe the difference between average velocity and instantaneous velocity. Provide a simple example to illustrate each concept. 1.5. A ball is thrown vertically upward, and its velocity function is $v(t) = 9.8t - 5$. Determine the instantaneous velocity of the ball when $t = 2$ s.

          Instantaneous Velocity:
1.1. An object moves along a straight path, and its position function is $s(t) = 2t^2 - 3t + 4$. Find
the instantaneous velocity of the object at $t = 3$ s.
1.2. A bicycle travels along a road, and its velocity-time graph is a straight line with a slope of
$2 \text{ m/s}^2$. Determine the instantaneous velocity of the bicycle at any time.
1.3. A car is initially at rest. Its velocity-time graph shows a constant positive slope of $5 \text{ m/s}^2$.
Calculate the instantaneous velocity after 4 s.
1.4. Describe the difference between average velocity and instantaneous velocity. Provide a simple
example to illustrate each concept.
1.5. A ball is thrown vertically upward, and its velocity function is $v(t) = 9.8t - 5$. Determine the
instantaneous velocity of the ball when $t = 2$ s.

Show more…

Instantaneous Velocity:
1.1. An object moves along a straight path, and its position function is s(t) = 2t^2 - 3t + 4. Find
the instantaneous velocity of the object at t = 3 s.
1.2. A bicycle travels along a road, and its velocity-time graph is a straight line with a slope of
2 m/s^2. Determine the instantaneous velocity of the bicycle at any time.
1.3. A car is initially at rest. Its velocity-time graph shows a constant positive slope of 5 m/s^2.
Calculate the instantaneous velocity after 4 s.
1.4. Describe the difference between average velocity and instantaneous velocity. Provide a simple
example to illustrate each concept.
1.5. A ball is thrown vertically upward, and its velocity function is v(t) = 9.8t - 5. Determine the
instantaneous velocity of the ball when t = 2 s.

Added by Brian C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Emily Anderson

09/02/2021

Step 1

Step 1: To find the instantaneous velocity of the object at t=3s, we need to find the derivative of the position function s(t)=2t^(2)-3t+4 with respect to time. Show more…

Show all steps

lock

Thanks for your feedback!

Instantaneous Velocity: 1.1. An object moves along a straight path, and its position function is s(t)=2t^(2)-3t+4. Find the instantaneous velocity of the object at t=3s. 1.2. A bicycle travels along a road, and its velocity-time graph is a straight line with a slope of 2(m)/(s^(2)). Determine the instantaneous velocity of the bicycle at any time. 1.3. A car is initially at rest. Its velocity-time graph shows a constant positive slope of 5(m)/(s^(2)). Calculate the instantaneous velocity after 4s. 1.4. Describe the difference between average velocity and instantaneous velocity. Provide a simple example to illustrate each concept. 1.5. A ball is thrown vertically upward, and its velocity function is v(t)=9.8t-5. Determine the instantaneous velocity of the ball when t=2s. Instantaneous Velocity: 1.1. An object moves along a straight path,and its position function is s(t) =2t2 3t+ 4.Find the instantaneous velocity of the object at t= 3 s. 1.2. A bicycle travels along a road, and its velocity-time graph is a straight line with a slope of 2 m/s2. Determine the instantaneous velocity of the bicycle at any time. 1.3. A car is initially at rest. Its velocity-time graph shows a constant positive slope of 5 m /s2. Calculate the instantaneous velocity after 4 s. 1.4. Describe the difference between average velocity and instantaneous velocity. Provide a simple example to illustrate each concept. 1.5.A ball is thrown vertically upward, and its velocity function is () = 9.8t 5. Determine the instantaneous velocity of the ball when t 2 s.

Play audio

Feedback

Powered by NumerAI

Emily Anderson and 52 other subject Physics 103 educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 In this example, we're going to be looking at the relationships between position, time, and velocity.

00:09 And we're going to do a little bit of extrapolating data from a graph.

00:13 So let's look at our graph.

00:17 All right.

00:17 And the first thing we want to do is try to describe the motion of the object here that's represented on the graph.

00:24 So we have some object and it starts at the origin.

00:28 So it starts at x equals zero, y equals zero.

00:35 Right, so time equals zero.

00:36 When time equals zero, our y -axis value equals zero.

00:41 So we're starting at, let's just say, grounds level.

00:46 All right, and we see as time increases, our y value increases, until we get to approximately a time of, let's see, call that seven seconds, that b.

01:03 All right, and then our y value starts to decrease.

01:07 All right.

01:11 So what this is saying is that we're looking at an object that has a positive velocity.

01:18 We know velocity is just the slope of the tangent line of a curve.

01:23 So i'll just use this as a quick example.

01:26 So the slope we can see is positive.

01:28 X is positive, y is positive.

01:30 So as x increases, y increases.

01:33 So it has a positive velocity, it flows down gradually, comes to a stop, and then starts to move with a negative velocity.

01:42 You can see that again.

01:43 This slope now is negative.

01:46 So as x increases y is decreasing.

01:52 Right.

01:52 So what this is describing, just for an example, is say you throw a ball straight up in the air, right? you throw it up with some initial velocity.

01:59 It moves in an upward direction.

02:01 Eventually comes to a stop and returns back.

02:03 Down to the ground.

02:06 And there's other examples i can use, but that's the simplest one...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later