Question

A drone flying at 4.82 m/s begins

to accelerate. It takes 24.8 s for it to
reach 7.09 m/s.
How far does the drone travel in
this time?
Ax = [?] m

Answer 1

The calculated distance traveled by the drone during acceleration is approximately
`\(199.14 \, \text{meters}\)`, consistent.

To find the distance traveled by the drone during acceleration, you can use the following kinematic equation:

`\[ v_f = v_i + a \cdot t \]`

Where:

-
`\( v_f \)` is the final velocity (7.09 m/s),

-
`\( v_i \)` is the initial velocity (4.82 m/s),

-
`\( a \)` is the acceleration,

-
`\( t \)`is the time taken (24.8 s).

Rearrange the equation to solve for acceleration
`(\( a \))`:

`\[ a = (v_f - v_i)/(t) \]`

Now, you can use the following kinematic equation to find the distance
`(\( s \))` traveled during acceleration:

`\[ s = v_i \cdot t + (1)/(2) \cdot a \cdot t^2 \]`

Plug in the values:

`\[ s = (4.82 \, \text{m/s} \cdot 24.8 \, \text{s}) + (1)/(2) \cdot \left((7.09 - 4.82)/(24.8)\right) \cdot (24.8 \, \text{s})^2 \]`

Now, let's calculate this:

`\[ s \approx 4.82 \, \text{m/s} \cdot 24.8 \, \text{s} + (1)/(2) \cdot 0.090725 \, \text{m/s}^2 \cdot (24.8 \, \text{s})^2 \]`

`\[ s \approx 119.416 + 79.724 \]`

`\[ s \approx 199.14 \, \text{meters} \]`

Therefore, the calculated distance traveled by the drone during acceleration is approximately
`\(199.14 \, \text{meters}\)`, consistent.

Answer 2

The drone travels approximately 199.14 meters in this time.

Step-by-step explanation:

To find the distance the drone travels, we can use the equation:

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

where d is the distance, u is the initial velocity, t is the time, and a is the acceleration.

In this case, the drone starts with an initial velocity of 4.82 m/s, accelerates for 24.8 s, and reaches a final velocity of 7.09 m/s. The acceleration can be found using the equation:

a = (v - u) / t

where v is the final velocity. Substituting the given values into the equation, we get:

a = (7.09 - 4.82) / 24.8

Simplifying the equation gives a = 0.0937 m/s^2.

Now we can plug in the values into the distance equation:

d = 4.82 * 24.8 + (1/2) * 0.0937 * (24.8)^2

Calculating the equation gives d ≈ 199.14 m.