Finding Time t for Instantaneous & Average Velocity: Particle Motion

[sammiyahc0]

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.

 

[Feodalherren]

Average velocity = (x2 - x1)/Δt

How do you find instantaneous velocity?

 

[sammiyahc0]

the derivative

 

[sammiyahc0]

what does x represent?

 

[Aelo]

The position. x2 - x1 is the change in position. Your object starts at one point, and ten seconds later, it's somewhere else. That somewhere else is x2.

 

[HallsofIvy]

what does x represent?

Your "s". The average speed, between t= 0 and t=10, is (s(10)- s(0))/(10 - 0). Calculate that, set it equal to s'(t) and solve for t.