Question

Hey, I'm trying to do some study for my exams this week, I'm just looking at a sample paper, I get the general idea, but I'm not quite sure on the wording of iii, iv and vi


b. A car passes a point p and applies its brakes at t=0 seconds. The car’s distance, s, from p at any subsequent time t is given by s = 20 t – 2 t2 where s is measured in metres and t in seconds.
Find
i. the distance of the car from p after 4 seconds
ii. the speed of the car at t = 4
iii. the car’s speed as it passed through p
iv. the time at which the car comes to rest
vi. the constant acceleration of car

Answer 1

sorry not good at this kind of math

Answer 2

It seems you're given
\[\large s(t) = 20t - 2t^2\]right?

Answer 3

This is what's called the position function.

Answer 4

The velocity (speed) function is simply the derivative of the position function with respect to time (t)
\[\large v(t) = \frac{d}{dt}s(t)=s'(t)=20-4t\]

Answer 5

And finally, the acceleration function is the derivative of the velocity function, or the second derivative of the position function, with respect to time...
\[\large a(t) = \frac{d}{dt}v(t)=\frac{d^2}{dt^2}s(t)=s''(t)=v \ '(t)=-4\]

Answer 6

So, I take it the questions are now readily doable? @Wilde1 :D

Answer 7

@terenzreignz - You've just saved me a lot of heartbreak on the last one, though I'm still puzzled by the wording of iii and vi, it's my understanding if iii is looking for the point p at which t = 0 then it'dd work out as v(0) = d / dt s(0) = 20 - 4(0) = 20

Answer 8

Okay, first off, you're asked for the speed (velocity) right?
So you use the function
v(t) = 20 - 4t

And at the point p, t = 0
So...
v(0) = 20

You were correct in your suspicions... :)
Don't doubt yourself XD

Answer 9

I've literally been looking at that for the last hour and I've been like "No, it can't be that simple."

Answer 10

Actually, just checked the time, three hours.

Answer 11

Well, it makes sense, right?
Though you doubted yourself... what did you expect the answer to (iii) would be?
0? :D

Answer 12

It makes sense, but I've been so useless at math for far too long and trusting my own intuitions when it comes to numbers hasn't fared well for me in the past :P
is
iv. the time at which the car comes to rest

20 - 4t = 0
4t = 20
t = 5 ?

Answer 13

Well, it seems your good intuition is coming back to you.
You are correct, by the way :)

Answer 14

By the way, why did you skip (v)
Your teacher not a big fan of five? :D

Answer 15

I'll be a Chemist yet :P *shakes fist*
Thank you very much for your help,

v. is related to the distance from p when it comes to a rest which I figured was just i. with 5 seconds instead of 4

Answer 16

ahh okay :)
Yes, you will be a Chemist!!! :D
Too bad I'm no good in Chemistry :3

Answer 17

Well if you ever need any help with Chemistry, I'm here to help :P, I wouldn't say I'm terrible at math, just that I tend to over complicate things in my head when I read the damn questions,

Answer 18

I'll be signing off for a bit... hopefully I won't encounter anything in Chemistry that would actually force me to ask a question on this site :D
Welcome to Openstudy, stick around, see if you can help some people out :)
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Terence out