- #1
Ammar w
- 28
- 0
Homework Statement
An object moves along the x-axis according to the equation x = 3.00t2 - 2.00t + 3.00 , where x is in meters and t is in seconds.
Determine :
(a) the average speed between t = 2.00 s and t = 3.00 s.
(b) the instantaneous speed at t = 2.00
(c) the average acceleration between t = 2.00 s and t = 3.00 s.
(d) the instantaneous acceleration at t = 2.00 s
(e) at what time is the object at rest?
Homework Equations
average speed = [itex]\frac{d(total distance travelled)}{\Delta t}[/itex]
instantaneous speed = [itex]\frac{dx}{dt}[/itex]
[itex]\overline{a}[/itex] (average acceleration) = [itex]\frac{\Delta v}{\Delta t}[/itex]
a (instantaneous acceleration) = [itex]\frac{dv}{dt}[/itex] = [itex]\frac{dx^2}{dt}[/itex]
The Attempt at a Solution
(a) I couldn't calculate the total distance.
(b) instantaneous speed = instantaneous velocity = [itex]\frac{dx}{dt}[/itex] = 6.00t - 2.00
instantaneous speed at t=2.00 = 6.00(2)-2.00 = 10 m/s
(c) [itex]\overline{a}[/itex] = [itex]\frac{\Delta v}{\Delta t}[/itex] = [itex]\frac{vf-vi}{1}[/itex] = [itex]\frac{v(3)-v(2)}{1}[/itex] = [itex]\frac{16-10}{1}[/itex] = 6 m/s2
(d) a = [itex]\frac{dx^2}{dt}[/itex] = 6 => a at 2.00s = 6 m/s2
(e) the rest means that v = 0
=> 6t-2=0
=>t=0.33 s //it seems wrong.