# Differentiation

• May 29th 2009, 03:26 PM
p4pri
Differentiation
Following formula shows the veloctiy, vms-1, at time t seconds for the first 8 seconds of motion:

v=(60t^2-5t^3)/64

Find the acceleration when t=8

I know you have to differentiate and i got 120t-15t^2
However, the mark scheme says to reduce the mark if 64 is left off - why would you leave 64 on?

Equally when I intergrate the formula, apparently 64 is not 64t but just 64, why?

Thanks Very Much
• May 29th 2009, 04:08 PM
skeeter
Quote:

Originally Posted by p4pri
Following formula shows the veloctiy, vms-1, at time t seconds for the first 8 seconds of motion:

v=(60t^2-5t^3)/64

Find the acceleration when t=8

I know you have to differentiate and i got 120t-15t^2
However, the mark scheme says to reduce the mark if 64 is left off - why would you leave 64 on?

Equally when I intergrate the formula, apparently 64 is not 64t but just 64, why?

Thanks Very Much

because of the constant multiple rule ...

$\displaystyle \frac{d}{dt}[k \cdot f(t)] = k \cdot f'(t)$

think of $\displaystyle k$ as $\displaystyle \frac{1}{64}$