Question

An object has an initial velocity of 19 m/s and a constant acceleration of 4.1 m/s^2. How long will it take before its final velocity is equal to three times its initial velocity?

Answer 1

Given:

• Initial velocity = 19 m/s

,

• Acceleration = 4.1 m/s²

Let's find how long it will take before its final velocity is equal to three times its initial velocity.

Apply the motion formula:

`v=u+at`

Where:

v is the final velocity

u is the initial velocity

a is the acceleration

t is the time.

Since we are to find the time it will take the final velocity to equal 3 times the initial velocity, we have:

v = 3u

Substitute 3u for v in the equation.

We have:

`3u=u+at`

Substitute values into the formula and solve for t:

`\begin{gathered} 3(19)=19+4.1t \\ \\ 57=19+4.1t \\ \text{ Subtract 19 from both sides} \\ 57-19=19-19+4.1t \\ \\ 38=4.1t \\ \\ \end{gathered}`

Divide both sides by 4.1:

`\begin{gathered} (38)/(4.1)=(4.1t)/(4.1) \\ \\ 9.17=t \\ \\ t=9.27\text{ s} \end{gathered}`

Therefore, it will take 9.27 seconds before its final velocity is equal to three times its initial velocity.

ANSWER:

9.27 s