Functions Module

[K.ourt]

Ok Ok...Ive a few questions for ya'll =)

1) A .5 kg ball is thrown vertically upward at a speed of 25 m/s. Its velocity, v(t) (in m/s), at time, t (in seconds), is given by v(t)=25-9.8t. It's kinetic energy, K(v) (in Joules), is given by K(v)=0.5v^2. Express the ball's kinetic energy as a function of time, K(t).

So, Im wondering if I figure out v(t) first, and then sub that into the kinetic energy (K(v)). But that would give me K(v), and I need K(t), so I need to figure out the time, right? I dont like the way its worded (exactly how it is up above is whats on my paper). It confuses me =p (I just needa know what goes where, I dont need it done for me. Hehe, unless you want to!!)





2) Maurice drove 400km from Edmonton to Battleford in one hour less time than it took Martin to drive the same route from Battleford to Edmonton. If Maurice drove 20 km/h faster than Martin, at what speed did each of them drive?

Ok, Im havin trouble coming up with the equation. Im thinkin x should be the speed that each of them drove (maybe?)? My mom and I cant figure out the exact equation, but Im pretty sure that it will have to be in the Maurice=Martin form. Uhm.. a little push in the right direction would be greatly appreciated. Hehe. (once again, Im not asking you to solve it for me guys, just give me a hint or something on where the x's go and such. hehe)


Thanks guys!!!

 

[stapel]

1) Plug the v(t) expression into K(v) wherever there is a "v". Simplify. This will give you K in terms of t.

2) Use the "d = rt" equation they gave you.

Martin:
distance: 400
rate: r
time: 400/r

Maurice:
distance: 400
rate: r + 20
time: 400/(r + 20)

(Maurice's time) was (Martin's time) less (one hour)

Translate into an equation, and solve.

Eliz.

 

[Gene]

You might want to correct the KE formula though. It is
(1/2)*m*v²

 

[soroban]

Hello, K.ourt!

2) Maurice drove 400km from Edmonton to Battleford in one hour less time
than it took Martin to drive the same route from Battleford to Edmonton.
If Maurice drove 20 km/h faster than Martin, at what speed did each of them drive?

This involves the familiar formula: . Distance .= .Speed x Time.

We are concerned with three quatities: Speed, Time, and Distance.

Usually, we are <u>given</u> one of quantities.
. . In this problem, we are given the distance: 400 km.

We are asked to <u>find</u> another quantity.
. . In this problem, we are asked to find their speeds.
. . Set up the x's.
. . . . x = Martin's speed.
. . . . x + 20 = Maurice's speed.

We usually build our equation from a fact given about the third quantity.
. . In this problem, the third quantity is Time.
. . We are told that Maurice's time is one hour less than Martin's.

To work with Time, we use this variation: . Time .= .Distance ÷ Speed


Maurice drove 400 km at x + 20 kph. .His time is: 400/(x + 20) hours.

Martin drove 400 km at x kph. .His time is: 400/x hours.

. . . "Maurice's time is one hour less than Martin's time"
. . . . . . . . . ↓ . . . . . ↓ . \_______________________/
. . . . . . . . 400 . . . . . . . . . . . 400
. . . . . . ---------- . . = . . . . . . ------ . - . 1 . . . . . . . there!
. . . . . . .x + 20 . . . . . . . . . . . .x