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sammiyahc0
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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.
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.sammiyahc0 said:what does x represent?
Instantaneous velocity is the velocity of an object at a specific moment in time. It is calculated by finding the slope of the tangent line on a position vs. time graph at that particular time.
Unlike average velocity, which is the total displacement divided by the total time, instantaneous velocity is the velocity at a specific instance in time. Average velocity takes into account the entire motion of an object, while instantaneous velocity focuses on a single point.
The formula for calculating instantaneous velocity is v = lim Δt→0 (Δx/Δt), where v is velocity, Δx is displacement, and Δt is change in time. Essentially, it is the change in position divided by the change in time as the change in time approaches zero.
Instantaneous velocity and acceleration are closely related. Acceleration is the rate of change of velocity, so the instantaneous velocity at a specific time can be used to calculate the acceleration at that same time.
Instantaneous velocity is important in physics because it allows us to understand the motion of objects at specific points in time. It also helps us to analyze and predict the behavior of objects in motion, and is a fundamental concept in many areas of physics, including kinematics, dynamics, and calculus-based mechanics.