Question

An object with an initial velocity of 2.0 m/s moves east along a straight and level path. The object then undergoes a constant acceleration of 1.80 m/s east for a period of 5.00 s. How far does the object move while it is accelerating?

Answer 1

The object moves 32.5 meters east while it is accelerating, based on the given initial velocity, constant acceleration, and time duration.

Step-by-step explanation:

To calculate the displacement of an object undergoing constant acceleration, we can use one of the kinematic equations derived from the principles of classical mechanics. Specifically, we can use the equation:

s = ut + 1/2at²

Where:

• s is the displacement
• u is the initial velocity
• a is the acceleration
• t is the time

Given an initial velocity (u) of 2.0 m/s, a constant acceleration (a) of 1.80 m/s², and a time (t) of 5.00 s, we substitute these values into the equation:

s = (2.0 m/s)(5.00 s) + 1/2(1.80 m/s²)(5.00 s)²

Calculating the displacement:

s = 10.0 m + 1/2(1.80 m/s²)(25.0 s²)

s = 10.0 m + 1/2(45.0 m)

s = 10.0 m + 22.5 m

s = 32.5 m

Therefore, the object moves 32.5 meters east while it is accelerating.