This should be easy... maybe I'm tired?

Hi,
I was able to do this fine yesterday, but for some odd reason, I can't seem to do them now.
Mechanics M1 - Generation motion in a straight line.
How do I solve this question? (Looking at what I did yesterday isn't helping :eek3:

)
Given that

v=t^2+12t+40

. Find the velocity when the acceleration is zero.
Thanks

Reply 1

around

What's the definition of acceleration? What does it mean for the acceleration to be 0?

Reply 2

SunGod87

v = t^2 + 12t + 40
a = dv/dt = 2t + 12

For the time at which the acceleration is zero:
a = 0 = 2t + 12
t = -6

So for the velocity at the time when the acceleration is zero:
v = (-6)^2 + 12(-6) + 40 = 36 - 72 + 40 = 4

Reply 3

CJN

Maybe differentiate it to find the acceleration, you know acceleration is 0 so you can find time t. Then in the original equation put that time in and get a velocty.

EDIT: beaten to it

Reply 4

04nunhucks

Aah, thanks everyone :smile:

But I now stuck on another question, second last one :/

Given that

x=10t-\frac{16}{\sqrt{t}}

, find the displacement and accel when velocity = 11ms-1
I've converted the 16 over root t to a normal fraction, i.e,

16\sqrt{t}^-1

Reply 5

04nunhucks

Hang on, am I missing something?

Reply 6

CJN

Assuming the x in your equation is meant to be v, first put in x = 11 to find t.

Then you can integrate it and put in t to find displacement, and differentiate it and put in t to find the acceleration.