Help Instantaneous velocity

In summary, the position of a particle moving in a straight line during a 10-second trip can be represented by the equation s(t) = 3t2 - 3t + 5 cm. To find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip, the derivative s'(t) = 6t - 3 can be used. However, the average velocity is defined as the change in position divided by the time elapsed, so more information is needed to solve for t.
  • #1
The position of a particle moving in a straight line during a 10–second trip is s(t) = 3t2 − 3t + 5 cm.Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip
 
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  • #2
Show us some attempt at least!
 
  • #3
s'(t)=6t-3=6(10)-3=57s instantenous velocity but I don't know how to get average
 
  • #4
Please don't post the same problem in different forums.

See, you've confused yourself because there may be different replies in your other post.
 
  • #5
I still need help.
 
  • #6
sammiyahc0 said:
s'(t)=6t-3=6(10)-3=57s instantenous velocity but I don't know how to get average

Average velocity is defined as change in position divided by time elapsed.
 

1. What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It is the rate of change of an object's position with respect to time at a particular instant.

2. How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a specific moment, while average velocity is the total displacement divided by the total time taken. Average velocity considers the entire motion of an object, while instantaneous velocity only looks at a specific instant.

3. How is instantaneous velocity calculated?

Instantaneous velocity can be calculated by finding the slope of the tangent line to the position-time graph at a specific point. It can also be calculated using the equation v=Δx/Δt, where Δx is the change in position and Δt is the change in time.

4. What is the unit of measurement for instantaneous velocity?

The unit of measurement for instantaneous velocity is meters per second (m/s) in the SI system or feet per second (ft/s) in the imperial system.

5. Why is instantaneous velocity important in physics?

Instantaneous velocity is important in physics because it helps us understand the motion of objects at a specific moment in time. It allows us to analyze the speed and direction of an object at a particular instant and make predictions about its future motion.

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