Question

Arrange the equations in the correct sequence to rewrite the formula for displacement,
d = 1/2 (v0 + v) to find v0. In the formula, d is displacement, v0 is the initial velocity, v is the final velocity, and t is the time.

2d/t = v0 + v
v0 = 2d/t + v
2d = (v0 + v)t
2t/d = v0 + v
v0 = 2d/t - v

Sequence:
1
↓
2
↓
3

Answer 1

From the given formula d = 1/2 (v0 + v)(t): I assume there must be a t, otherwise the formula is inconsistent dimensionally.
1. We multiply both sides by 2:
2d = (v0 + v)(t) - this is the 3rd choice
2. Divide both sides by t:
2d/t = v0 + v - this is the 1st choice
3. Subtract v from both sides:
2d/t - v = v0
v0 = 2d/t - v - this is the 5th equation

Answer 2

Answer: 1. $2d=(v_0+v)t$

2. $\frac{2d}{t}=v_0+v$

3. $v_0=\frac{2d}{t}-v$

Step-by-step explanation:

Given: The formula for displacement, $d=\frac{1}{2}(v_0+v)t$

to find $v_0$.

In the formula, d is displacement, $v_0$ is the initial velocity, v is the final velocity, and t is the time.

Multiply 2 on both sides, we get

$2d=(v_0+v)t$

Divide t on sides, we get

$\frac{2d}{t}=v_0+v$

Subtract v on both sides we get,

$v_0=\frac{2d}{t}-v$

The equations in the correct sequence to rewrite the formula for displacement is

1. $2d=(v_0+v)t$

2. $\frac{2d}{t}=v_0+v$

3. $v_0=\frac{2d}{t}-v$