Posted by **Eva** on Thursday, September 11, 2008 at 5:31pm.

A particle moves at varying velocity along a line and s= f(t) represents the particle's distance from a point as a function of time, t. sketch a graph for f if the average velocity of the particle between t=2 and t=6 is the same as the instantaneous velocity at t=5.

I know that instantaneous velocity is calculated as s(a+h)-s(a)/h but i don't understand what to put in for h. I'm stuck at this point and would appreciate any guidance on what to do next. thanks so much!!!

- Calc I -
**Damon**, Thursday, September 11, 2008 at 8:01pm
" I know that instantaneous velocity is calculated as s(a+h)-s(a)/h ...."

=============================

Well sort of.

The limit of that expression as s goes to zero is the instantaneous velocity. It is also the slope of your curve at t = 5.

However the expression as you wrote it is the average velocity or slope of the curve between t = 2 and t = 5

Therefore draw a slope and s value at t = 5

To make it really simple, sketch a straight line with that slope from t = 2 to t = 6

Of course the curve could take all kinds of twists and turns instead of what we sketched, but the basic idea is that at t = 5 the slope is the same as the slope of a straight line from t = 2 to t = 5

## Answer This Question

## Related Questions

- Calculus - A particle moves at varying velocity along a line and s=f(t) ...
- Physics - A particle starts from the origin at t = 0 and moves along the ...
- Math - Context: The function v(t) represents the velocity of a particle moving ...
- Calc - a partial moves along the x-axis so that its velocity at time t, for 0<...
- physics - a particle covers 1/2 distance between A and B with a velocity V0. ...
- help math - a partial moves along the x-axis so that its velocity at time t, for...
- math - A particle moves along straight line such that its displacement S meters...
- calculus - 5. A particle moves along the y – axis with velocity given by v(t)=...
- Calculus - The Question: A particle moves along the X-axis so that at time t >...
- Calculus - A particle starts at the point (5,0) at t=0 and moves along the x-...

More Related Questions