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Suppose the initial position of an object is zero, the starting velocity is 3 m/s and the final velocity was 10 m/s. The

object moves with constant acceleration. Which part of a velocity vs. time graph can be used to calculate the
displacement of the object?

User Eselk
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Answer:

Explanation: To calculate the displacement of an object moving with constant acceleration, we can use the following kinematic equation:

d = (1/2)at^2 + v0t

where d is the displacement of the object, a is the constant acceleration, t is the time elapsed, and v0 is the initial velocity of the object.

In this case, we know the initial velocity v0 = 3 m/s and the final velocity vf = 10 m/s. We also know that the object moves with constant acceleration, so we can use the following equation to relate the initial and final velocities to the acceleration and displacement:

vf^2 = v0^2 + 2ad

Solving for d, we get:

d = (vf^2 - v0^2) / (2a)

Substituting the given values, we get:

d = (10^2 - 3^2) / (2a) = 91 / (2a)

Therefore, to calculate the displacement of the object, we need to determine the value of the acceleration.

We can use the velocity vs. time graph to find the acceleration of the object. The slope of the velocity vs. time graph represents the acceleration of the object, since acceleration is the rate of change of velocity with respect to time.

Since the initial position of the object is zero, the velocity vs. time graph will pass through the origin. Therefore, we can use the part of the graph between the initial time t=0 and the final time when the velocity is 10 m/s. This part of the graph will be a straight line with positive slope, representing the constant acceleration of the object.

We can calculate the slope of this line by finding the change in velocity and dividing by the time elapsed:

a = (vf - v0) / t

Substituting the given values, we get:

a = (10 - 3) / t

Therefore, the acceleration of the object is 7/t, where t is the time elapsed between the initial and final velocities.

Substituting this value for a into the expression for displacement, we get:

d = 91 / (2(7/t)) = (91t) / 14

Therefore, the part of the velocity vs. time graph between t=0 and the final time can be used to calculate the displacement of the object using the equation d = (91t) / 14.

User Perrie
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