Distance Traveled

[legacyofpiracy]

Alright so we just began a new chapter in calculus class and I thought i'd try out the homework. It deals with definite integrals and all the RRAM, MRAM, LRAM stuff and I am still kind of shakey. I was wondering if anyone could help me along in this problem:

At time t=0 I set off along the highway, and for the first 6 minutes my speed increases at the constant rate of 28 km/h per minute. I then maintain this speed for the rest of the journey.

a) After how many minutes is my speed 126 km/h?
b) How many km do I travel in the first hour?
c) After how many minutes have I gone 100 km?

any tips would be appreciated

 

[stapel]

...we just began a new chapter....all the RRAM, MRAM, LRAM stuff

:shock:

Um... what?

Please reply with definitions. Thank you.

Eliz.

 

[legacyofpiracy]

Oops sorry :roll: I probably should have clarified that. The chapter deals with finding the area beneath a curve. In order to estimate this, a number of rectangles are drawn beneath the curve and the area of these rectangles is taken. To do this they use the Rectangular Approximation Method (RAM). The RRAM, LRAM etc refers to which side of the rectangle you take the height of (left right or middle) and this varies according to the slope of the curve.

 

[Daniel_Feldman]

...we just began a new chapter....all the RRAM, MRAM, LRAM stuff

:shock:

Um... what?

Please reply with definitions. Thank you.

Eliz.

I think he/she is talking about area approximations-left, right, and midpoint Riemann sums. Just a guess.

Here's what I don't get

"At time t=0 I set off along the highway, and for the first 6 minutes my speed increases at the constant rate of 28 km/h per minute. I then maintain this speed for the rest of the journey."

What speed, 28 km/h or the speed you reach after 6 minutes. Are you saying that yor speed increases at a rate of 28 km/h and then suddenly drops to 28km/h? Please clarify.

 

[soroban]

Here's my interpretation of the problem . . .

At time t=0 I set off along the highway

I would assume that: \(\displaystyle s(0)\,=\,0\) and \(\displaystyle v(0)\,=\,0\).

and for the first 6 minutes my speed increases at the constant rate of 28 km/h per minute.

For \(\displaystyle t\,\leq\,6,\;v(t)\,=\,28t\)

I then maintain this speed for the rest of the journey.

The rest of the trip is at \(\displaystyle 168\) km/hr.