A race car moves such that its position fits the relationshipx = (5.5 m/s)t + (0.65 m/s3)t3where x is measured in meters and t in seconds.(b) Determine the instantaneous velocity of the car att = 3.8 s,using time intervals of 0.40 s, 0.20 s, and 0.10 s. (In order to better see the limiting process keep at least three decimal places in your answer.) Δt = 0.40 s m/s (Use the interval fromt = 3.60 sto 4.00 s.)Δt = 0.20 s m/s (Use the interval fromt = 3.70 sto 3.90 s.)Δt = 0.10 s m/s (Use the interval fromt = 3.75 sto 3.85 s.) ### Position-Time Graph#### Description:The graph above is a position-time graph that depicts the position \( x \) in meters (m) as a function of time \( t \) in seconds (s). #### Axes:- **Horizontal Axis (x-axis):** Represents time \( t \) in seconds (s), ranging from 0 to 6 seconds.- **Vertical Axis (y-axis):** Represents position \( x \) in meters (m), ranging from 0 to 180 meters.#### Data Points:- At \( t = 0 \, \text{s} \), \( x \) is approximately 0 meters.- At \( t = 1 \, \text{s} \), \( x \) is approximately 10 meters.- At \( t = 2 \, \text{s} \), \( x \) is approximately 40 meters.- At \( t = 3 \, \text{s} \), \( x \) is approximately 80 meters.- At \( t = 4 \, \text{s} \), \( x \) is approximately 130 meters.- At \( t = 5 \, \text{s} \), \( x \) is approximately 170 meters.- At \( t = 6 \, \text{s} \), \( x \) is approximately 180 meters.#### Interpretation:The curve indicates that as time progresses, the position \( x \) increases. Notably, the curve is non-linear and appears to be parabolic, suggesting that the position \( x \) increases at an accelerating rate as time goes on. This type of graph is often indicative of an object undergoing uniformly accelerated motion. #### Educational Context:This graph may be used to illustrate concepts in kinematics, such as uniformly accelerated motion, displacement, and the relationship between distance and time. It is particularly useful for understanding how acceleration affects the position of an object over time.

It is given that, x = 5.5t + 0.65t3m

Answered: A race car moves such that its position…

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)...

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A race car moves such that its position fits the relationship

x = (5.5 m/s)t + (0.65 m/s³)t³

where x is measured in meters and t in seconds.

(b) Determine the instantaneous velocity of the car at

t = 3.8 s,

using time intervals of 0.40 s, 0.20 s, and 0.10 s. (In order to better see the limiting process keep at least three decimal places in your answer.)

Δt = 0.40 s	m/s (Use the interval from t = 3.60 s to 4.00 s.)
Δt = 0.20 s	m/s (Use the interval from t = 3.70 s to 3.90 s.)
Δt = 0.10 s	m/s (Use the interval from t = 3.75 s to 3.85 s.)

### Position-Time Graph

#### Description:
The graph above is a position-time graph that depicts the position \( x \) in meters (m) as a function of time \( t \) in seconds (s).

#### Axes:
- **Horizontal Axis (x-axis):** Represents time \( t \) in seconds (s), ranging from 0 to 6 seconds.
- **Vertical Axis (y-axis):** Represents position \( x \) in meters (m), ranging from 0 to 180 meters.

#### Data Points:
- At \( t = 0 \, \text{s} \), \( x \) is approximately 0 meters.
- At \( t = 1 \, \text{s} \), \( x \) is approximately 10 meters.
- At \( t = 2 \, \text{s} \), \( x \) is approximately 40 meters.
- At \( t = 3 \, \text{s} \), \( x \) is approximately 80 meters.
- At \( t = 4 \, \text{s} \), \( x \) is approximately 130 meters.
- At \( t = 5 \, \text{s} \), \( x \) is approximately 170 meters.
- At \( t = 6 \, \text{s} \), \( x \) is approximately 180 meters.

#### Interpretation:
The curve indicates that as time progresses, the position \( x \) increases. Notably, the curve is non-linear and appears to be parabolic, suggesting that the position \( x \) increases at an accelerating rate as time goes on. This type of graph is often indicative of an object undergoing uniformly accelerated motion.

#### Educational Context:
This graph may be used to illustrate concepts in kinematics, such as uniformly accelerated motion, displacement, and the relationship between distance and time. It is particularly useful for understanding how acceleration affects the position of an object over time.

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