A mysterious rocket-propelled object of mass.. A mysterious rocket-propelled object of mass 45.0 kg is initially at rest in the middle of the horizontal, frictionless surface of an ice-covered lake. Then a force directed east and with magnitude ` F(t) = (16.8N/s)t` is applied. How far does the object travel in the first 5.00 s after the force is applied?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Let's consider Newton's second law to solve this problem:

` ` `F = ma`

Now, let's substitute our values for mass and force:

`16.8 t = 45.0*a`

Solving for acceleration (and simplifying the fraction):

`a = 28/75t `

Now, let's consider that acceleration is a function of time. Also, remember that velocity will be the antiderivative of acceleration. So, let's solve for velocity:

`v(t) = int_0^t 28/75tau d tau`

Solving the integral:

`v(t) = 28/75 t^2/2 + v_0 = 14/75 t^2 + v_0`

To continue, we'll need to find that initial velocity. Thankfully the...

(The entire section contains 260 words.)

Unlock This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial
Approved by eNotes Editorial Team