Three students derive the following equations in which x refers to distance traveled, v the speed, a the acceleration (m/s^2), and t the time, and the subscript (0) means a quantity at time t=0: a) x=vt^2 + 2at, b) x=v0t+1/2at^2, and c) x=v0t+2at^2. Which of these could possibly be correct according to a dimensional check?

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30-01-2020
Physics

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Three students derive the following equations in which x refers to distance traveled, v the speed, a the acceleration (m/s^2), and t the time, and the subscript (0) means a quantity at time t=0: a) x=vt^2 + 2at, b) x=v0t+1/2at^2, and c) x=v0t+2at^2. Which of these could possibly be correct according to a dimensional check?

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Teebhabzie Teebhabzie · Answer 1 · 2020-02-02T23:23:18+01:00

Answer:

B) and C)

Explanation:

Dimensional check involves using the units of the fundamental quantities, like mass to verify the accuracy of a formula or model.

For this case, the quantities required are Length and Time. Their units are Metre (m) and Seconds (s) respectively.

Since x refers to Distance, v refers to velocity, a refers to acceleration and t refers to time,

A) x = vt² + 2at

=> m = (m/s * s²) + (m/s² * s)

m = ms + m/s

The units are unbalanced, hence, it is not dimensionally correct.

B) x = v₀t + 2at²

=> m = (m/s * s) + (m/s² * s²)

m = m + m

The units are balanced, hence, it is dimensionally correct.

C) x = v₀t + ¹/₂at²

=> m = (m/s * s) + (m/s² * s²)

m = m + m

The units are balanced, hence, it is dimensionally correct.

jayilych4real jayilych4real · Answer 2 · 2022-04-05T14:31:06+02:00

The answer choices which could possibly be correct according to a dimensional check are:

b) x=v0t+1/2at^2,
c) x=v0t+2at^2

What is Dimensional Check?

This refers to the use of fundamental quantities which are used to prove the authenticity of a model

Here, we would make use of length and time and their SI units are metres and seconds

X refers to Distance,
v refers to velocity,
a refers to acceleration
t refers to time,

Using elimination method:

A) x = vt² + 2at

=> m = (m/s * s²) + (m/s² * s)

m = ms + m/s

These units are unbalanced, hence, it is not dimensionally correct.

B) x = v₀t + 2at²

=> m = (m/s * s) + (m/s² * s²

m = m + m

The units are balanced, hence, it is dimensionally correct.

C) x = v₀t + ¹/₂at²

=> m = (m/s * s) + (m/s² * s²)

m = m + m

The units are balanced, hence, it is dimensionally correct.

Therefore, the correct answers are options B and C