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# Method of Subsitution : Velocity from Displacement and Acceleration

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In science, we calculate the displacement of an object (how far it travels) and the velocity of an object (how fast it is moving) using the displacement equation and the velocity equation.

where
x is the displacement of the object, measured in meters
t is the amount of time that we analyze the movement of the object, measured in seconds
v0 is the initial velocity of the object, i.e. the velocity of the object at the beginning of our analysis, measured in meters per second (m/s).
v is the final velocity of the object, i.e. the velocity of the object at the end of the time period t. The final velocity is measured in meter per second (m/s).

a is the acceleration experienced by the object, i.e. the rate at which the velocity is changing, measured in meters per square second (m/s2).

Problem
A car that is moving with an initial velocity of 4 m/s experiences an acceleration of 6 m/s2. Find the final velocity of the car after it has moved a distance of 7 meters while experiencing this acceleration.

Use the method of substitution.

##### Solution Summary

Velocity is found from displacement and acceleration.

##### Solution Preview

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In science, we calculate the displacement of an object (how far it travels) and the velocity of an object (how fast it is moving) using the displacement equation and the velocity equation.

where
x is the displacement of the object, measured in meters
t is the amount of time that we analyze the movement of the object, measured in seconds
v0 is the ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
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• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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