# Math Help - velocity and speed

1. ## velocity and speed

Equation is: x = 12t - t².
Calculate the average velocity and the average speed.

So far I have this.
v = 12 - 2t

Can the answer be determined from just this info? Or is smt missing? (My teacher is fond of making errors in questions....grrrr)

thanks

2. Originally Posted by jacs
Equation is: x = 12t - t².
Calculate the average velocity and the average speed.

So far I have this.
v = 12 - 2t

Can the answer be determined from just this info? Or is smt missing? (My teacher is fond of making errors in questions....grrrr)

thanks
What is your equation above supposed to represent?

the area in red isn't right becuase $x-x^2$ can't be simplified.

3. x is the equation of rectilinear motion, displacement x, in terms of t, time

usually we use this kind of thing to find instantaneous velocity or acceleration. I have not seen a question before on average speed or velocity without a specific time given.

4. Originally Posted by jacs
Equation is: x = 12t - t².
Calculate the average velocity and the average speed.

So far I have this.
v = 12 - 2t

Can the answer be determined from just this info? Or is smt missing? (My teacher is fond of making errors in questions....grrrr)

thanks
v = 12 - 2t is the instantaneous velocity.

Given a specific time interval:

Average velocity = $\frac{1}{t-t_0} \int_{t_0}^t \, dt (12 - 2t)$

Average speed = $\frac{1}{t-t_0} \int_{t_0}^t \, dt |12 - 2t|$

-Dan

5. thanks Dan, i understand the general expression, it makes sense, cheers.