Help on Instantaneous Velocity

In summary, the instantaneous acceleration at 4 s is 1.33 m/s2 and the instantaneous acceleration at 7 s is 0 m/s2. This can be calculated using the equation for average acceleration, which is equal to the slope of the velocity-time curve at any point.
  • #1
Leeee
5
0

Homework Statement


2je4m06.png

(X-Axis = Time)

1. Find the instantaneous acceleration at 4 s.
Answer in units of m/s2.

2. Find the instantaneous acceleration at 7 s.
Answer in units of m/s2.

Homework Equations


Unknown, I'm assuming you'll use:
Acceleration Average = Delta V(final)-V(initial)/Delta T

The Attempt at a Solution


I've used the equation above ^ and I've gotten for
1.) 3.1 - (-4)/4 = 1.775
2.) I'm assuming Zero considering the object is not moving.

Any help would be great, I'm not quite sure how to do these correctly, so guidance or reassurance would be great. Thanks.
 
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  • #2
You have the correct idea. Though for part 'a' you made a small mistake the time that elapses is only 3s so the acceleration=(4/3)=1.33m/s^2

The idea is that instantaneous acceleration is equal to the slope of the velocity-time curve at any point. Thus it is a derivative...but since the slope for part 'a' is a constant that means that the instantaneous acceleration over that whole portion is also a constant that can be calculated using the equation for average acceleration.

Likewise part 'b' is zero as you predicted, but not because the velocity is zero...it is because the slope is zero.
 
  • #3
kjohnson said:
You have the correct idea. Though for part 'a' you made a small mistake the time that elapses is only 3s so the acceleration=(4/3)=1.33m/s^2

The idea is that instantaneous acceleration is equal to the slope of the velocity-time curve at any point. Thus it is a derivative...but since the slope for part 'a' is a constant that means that the instantaneous acceleration over that whole portion is also a constant that can be calculated using the equation for average acceleration.

Likewise part 'b' is zero as you predicted, but not because the velocity is zero...it is because the slope is zero.

Thank you, very much appreciated.
 

1. What is instantaneous velocity?

Instantaneous velocity is the rate of change of an object's position at a specific moment in time. It is the velocity at an exact instant, as opposed to average velocity which is the overall change in position over a certain time period.

2. How is instantaneous velocity calculated?

Instantaneous velocity is calculated by taking the derivative of an object's position function with respect to time. This means finding the slope of the tangent line at a specific point on the position-time graph.

3. How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a single moment in time, while average velocity is the overall change in position over a certain time period. Instantaneous velocity takes into account any changes in direction or speed that may occur during that specific moment, while average velocity only considers the overall change.

4. Can instantaneous velocity ever be negative?

Yes, instantaneous velocity can be negative. This means that the object is moving in the opposite direction of the positive direction assigned on the position-time graph. It is important to note that this does not necessarily mean the object is slowing down, as velocity takes into account both speed and direction.

5. What is the difference between instantaneous velocity and instantaneous speed?

Instantaneous velocity and instantaneous speed are often used interchangeably, but they have different meanings. Instantaneous velocity includes both the magnitude (speed) and direction of an object's motion at a specific moment, while instantaneous speed only refers to the magnitude of an object's instantaneous velocity without considering its direction.

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