Finding velocity/distance from acceleration

[Tankertert]

Homework Statement

Hi guys. New here.

Im doing some last minute revision and i have a question I am stuck on.

an objects acceleration a in ms^-1 at time t seconds is shown by

a(t) = 6t + ∏cos(2∏ t), where t ≥ 0

if objects initial velocity is 3ms^-1, find:

a) objects velocity after 2 seconds

b) distance object travels in first 5 seconds.

If you can show me your answers and how you solved the question so i can see how you did it, that would be amazing. thank you!

Homework Equations

The Attempt at a Solution

i firstly tried substituting the time into solve, but that only gives me the acceleration and i need the velocity. and i have no idea on how to try and even get the second one.

 

[Infinitum]

Homework Statement

Hi guys. New here.

Im doing some last minute revision and i have a question I am stuck on.

Hi Tankertert, welcome to PF!

If you can show me your answers and how you solved the question so i can see how you did it, that would be amazing. thank you!

It would be better if you show us what you did, and we try guiding you to the answer.
Read : https://www.physicsforums.com/showthread.php?t=94379

i firstly tried substituting the time into solve, but that only gives me the acceleration and i need the velocity. and i have no idea on how to try and even get the second one.

Do you know basic calculus? If yes, what is the definition of instantaneous acceleration? and instantaneous velocity?

 

[Tankertert]

All i have done was sub 2 into a(t) = 6t + ∏cos(2∏ t) but i don't know how that would help me.

acceleration is velocity over time yes?
and velocity is distance over time?

 

[Matt4936]

For the first question you would multiply the acceleration by the time.

For the second question you would get the velocity and multiply that by the time.

Also acceleration is ms^-2 not -1. I'm sure that was just a typo but I'm just making sure.

 

[Matt4936]

For the first question you would multiply the acceleration by the time.

For the second question you would get the velocity and multiply that by the time.

Also acceleration is ms^-2 not -1. I'm sure that was just a typo but I'm just making sure.

 

[Infinitum]

All i have done was sub 2 into a(t) = 6t + ∏cos(2∏ t) but i don't know how that would help me.

acceleration is velocity over time yes?
and velocity is distance over time?

Although true, those are a bit vague definitions. Can you express the same mathematically, for instantaneous velocity/accelerations?

 

[Infinitum]

For the first question you would multiply the acceleration by the time.

This would work if the acceleration was constant, which it isn't...

 

[Matt4936]

That means that you would have to integrate the acceleration function to get the velocity function and then substitute time in?

 

[Infinitum]

That means that you would have to integrate the acceleration function to get the velocity function and then substitute time in?

There we go!