For constant acceleration, how does the average velocity for an interval compare with the instantaneous velocity at half-time in the interval?

For constant acceleration in one direction, they are the same

A truck moves 70m east, then moves 120m west, and finally moves east again a distance of 90 m. If east is chosen as the positive direction, what is the trucks resultant displacement?

opps sorry Lina I thought I could post a question here...mybad!

To compare the average velocity and instantaneous velocity for a constant acceleration, we first need to understand the definitions of average velocity and instantaneous velocity.

Average Velocity: The average velocity is defined as the displacement (change in position) divided by the time interval. Mathematically, it can be represented as:

Average velocity = (Change in position) / (Time elapsed)

Instantaneous Velocity: The instantaneous velocity is the velocity of an object at a specific instant or point in time. It is the rate of change of position with respect to time at that particular moment.

Now, for a constant acceleration scenario, if we consider an interval of time:

1. Average Velocity: To find the average velocity over the entire interval, we calculate the change in position (displacement) divided by the total time taken.

2. Instantaneous Velocity at Half-Time: To find the instantaneous velocity at half-time in the interval, we need to consider the velocity of the object at that specific moment. This can be calculated using the kinematic equations of motion. One of the most commonly used equations is:

V = u + at

where:
V is the final velocity,
u is the initial velocity,
a is the acceleration, and
t is the time taken.

In this case, we will need to calculate the instantaneous velocity at the halfway point of the interval, which would be t/2.

Now, to compare the average velocity and instantaneous velocity at half-time in the interval for constant acceleration:

If the acceleration is constant, the average velocity over the entire interval will be equal to the instantaneous velocity at half-time in the interval. This is because in constant acceleration scenarios, the velocity changes linearly with time.

Therefore, if you have the value of acceleration (a), initial velocity (u), and the time interval (t), you can calculate the instantaneous velocity at half-time using the equation mentioned above, and it will be equal to the average velocity for that interval.