An object moves along the x axis according to the equation x(t) = (2.90t2 - 2.00
ID: 1961085 • Letter: A
Question
An object moves along the x axis according to the equation
x(t) = (2.90t2 - 2.00t + 3.00) m, where t is in seconds.
(a) Determine the average speed between t = 3.40 s and t = 4.70 s.
_____________m/s
(b) Determine the instantaneous speed at t = 3.40 s and at t = 4.70 s.
_____________m/s (t = 3.40)
_____________m/s (t = 4.70)
(c) Determine the average acceleration between t = 3.40 s and t = 4.70 s.
_____________m/s2
(d) Determine the instantaneous acceleration at t = 3.40 s and t = 4.70 s.
_____________m/s2 (t = 3.40)
_____________m/s2 (t = 4.70)
Explanation / Answer
average speed can be determined by finding the displacement and dividing it by time x=(2.902*t^2-2t+3) a) at t=3.4 x=(2.902*3.4*3.4-2*3.4+3)=29.74 at t=4.7 x=64.10-9.4+3=57.7 avg speed=(57.7-29.74)/(4.7-3.4)=27.91/1.3=21.47 b)instantaneous velocity v=dx/dt=2.902*2t-2=5.804t-2 at t=3.4, v=17.72 at t=4.7, v=27.26 c) avg acceleration a=(v2-v1)/(t2-t1)=(27.26-17.71)/(4.7-3.4) =7.346 d) instantaneous acceleration a=dv/dt=5.804