An object moves along the x axis according to the equation x = 3.30 t 2 2.00 t +
ID: 1406177 • Letter: A
Question
An object moves along the x axis according to the equation
x = 3.30t2 2.00t + 3.00,
where x is in meters and t is in seconds.
(a) Determine the average speed between t = 2.20 s and t = 4.20 s.
m/s
(b) Determine the instantaneous speed at t = 2.20 s.
m/s
Determine the instantaneous speed at t = 4.20 s.
m/s
(c) Determine the average acceleration between t = 2.20 s and t = 4.20 s.
m/s2
(d) Determine the instantaneous acceleration at t = 2.20 s.
m/s2
Determine the instantaneous acceleration at t = 4.20 s.
m/s2
(e) At what time is the object at rest?
s
Explanation / Answer
v(t)=dx/dt
=d/dt(3.30t2 2.00t + 3.00)
=6.6t-2 m/sec
(a) the average speed between t = 2.20 s and t = 4.20 s
v(2.20)=6.6*2.20-2
=12.52 m/sec
v(4.20)=6.6*4.20-2
=25.72 m/sec
v(avg)=12.52+25.72/(4.20-2.20)
=19.12 m/sec--answer a
b)v(2.20)=v(2.20)=6.6*2.20-2
=12.52 m/sec
c)v(4.20)=
v(4.20)=6.6*4.20-2
=25.72 m/sec
c)a=dv/dt
=d/dt(6.6t-2)
=6.6
a = dv/dt = 6.6m/s^2 = constant
d) same as c as accleration is constant
a=6.6m/s^2
e)when v=0
now by taking dx/dt =0
dx/dt = 6.6t-2=0
6.6t=2
t=2/6.6
t=0.3 sec