hey guys i got my maths exam in two days and need urgent help in the kinematics area.

i get some of the basic stuff but anyways the question i'm struggling with is

Particle moves in a straight line so its position x cm relative to O at time t seconds (t0)
is given by x=t
²-7t+12
FIND
a. initial position
t=0
so therefore x=
0²-7(0)+12
x=12 cm to right of O

b. position at t=5
so therefore
x=5
²-7(5)+12
x=25-35+12
x=2 cm to the right of O when t=5
c. initial velocity
d. when and where velocity = 0
e. average velocity in the first 5s
f. average speed in the first 5s

alright the ones in red are the ones im sturggling with

anyone help would be greatly appreciated... thanks a lot guys and girls

2. Originally Posted by jimzer
hey guys i got my maths exam in two days and need urgent help in the kinematics area.

i get some of the basic stuff but anyways the question i'm struggling with is

Particle moves in a straight line so its position x cm relative to O at time t seconds (t0)
is given by x=t²-7t+12
FIND
a. initial position
t=0
so therefore x=0²-7(0)+12
x=12 cm to right of O
b. position at t=5
so therefore
x=5²-7(5)+12
x=25-35+12
x=2 cm to the right of O when t=5
c. initial velocity
The velocity is:

$\frac{d}{dt}x=2t-7$

So the initial velocity is:

$x_0 = -7$

d. when and where velocity = 0
e. average velocity in the first 5s
f. average speed in the first 5s
You should be able to do d. yourself.

e. The average velocity in the first 5 seconds is the change in position
in those five seconds divided by 5, so:

$
\bar{v}_{(0,5)} = \frac{x_{t=5}-x_{t=0}}{5}
$

f. The average speed is the average of |v| over the interval.

RonL

3. thanks a lot for the reply man! really appreciate it

but what i dont get is how you got

x=t²-7t+12

to become

2t-7

how does the

(d/dt)x formula work?

4. Originally Posted by jimzer
thanks a lot for the reply man! really appreciate it

but what i dont get is how you got

x=t²-7t+12

to become

2t-7

how does the

(d/dt)x formula work?
Calculus - differentiation of polynomials.

RonL

5. Originally Posted by jimzer
thanks a lot for the reply man! really appreciate it

but what i dont get is how you got

x=t²-7t+12

to become

2t-7

how does the

(d/dt)x formula work?
If you don't know that you have no business to be trying to answer this question. There's no way to do this problem without Calculus.

Edit: Well, I suppose you could do it using the basic kinematics equations for motion with constant acceleration, but to expect a student to come up with the solution on their own would be like expecting Aristotle to come up with Kepler's Laws: in principle he could have done it, but it wouldn't be very likely.

-Dan