# Acceleration & Velocity

• Mar 7th 2010, 12:19 PM
rawkstar
Acceleration & Velocity
T 0 2 4 6 8
A(t) 2 3 4 3 2

The table for the acceleration of a particle from 0 to 8 seconds is given in the table aove. if the velocity at t=0 is 4 feet per second, the approximation value of the velocity, in feet per second, at t=8 seconds using Riemann Sum with four divisions of equal length is?
• Mar 7th 2010, 01:12 PM
skeeter
Quote:

Originally Posted by rawkstar
T 0 2 4 6 8
A(t) 2 3 4 3 2

The table for the acceleration of a particle from 0 to 8 seconds is given in the table aove. if the velocity at t=0 is 4 feet per second, the approximation value of the velocity, in feet per second, at t=8 seconds using Riemann Sum with four divisions of equal length is?

left or right Riemann sum?

left sum approximation ...

$\displaystyle \int_0^8 a(t) \, dt \approx 2[a(0) + a(2) + a(4) + a(6)]$

right sum approximation ...

$\displaystyle \int_0^8 a(t) \, dt \approx 2[a(2) + a(4) + a(6) + a(8)]$

remember that either will be an estimate for $\displaystyle \Delta v$
• Mar 7th 2010, 01:47 PM
rawkstar
so what do i have to do to approximate the velocity at t=8?
• Mar 7th 2010, 01:51 PM
skeeter
Quote:

Originally Posted by rawkstar
so what do i have to do to approximate the velocity at t=8?

$\displaystyle v(0) + \int_0^8 a(t) \, dt = v(8)$
• Mar 7th 2010, 01:57 PM
rawkstar
i think i can take it over from here
thank you skeeter