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
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.
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.
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.
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.
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.