An object moves along the x axis according to the equation x = 3.75t2 2.00t + 3.
ID: 1523478 • Letter: A
Question
An object moves along the x axis according to the equation x = 3.75t2 2.00t + 3.00, where x is in meters and t is in seconds.
(a) Determine the average speed between t = 3.40 s and t = 5.30 s.
_____m/s
(b) Determine the instantaneous speed at t = 3.40 s. m/s Determine the instantaneous speed at t = 5.30 s.
_______m/s
(c) Determine the average acceleration between t = 3.40 s and t = 5.30 s.
_________m/s2
(d) Determine the instantaneous acceleration at t = 3.40 s. m/s2 Determine the instantaneous acceleration at t = 5.30 s.
_______m/s2
(e) At what time is the object at rest?
_____s
Explanation / Answer
a) Given Equation
x(t) = 3.75t^2 2.00t + 3.00,
Therefore
x(3.4) = 3.75*3.4^2 - 2*3.4 + 3
x(3.4) = 39.55
x(5.3) = 3.75*5.3^2 - 2*5.3 + 3
x(5.3) = 97.74
Vavg = x(5.-3) - x(3.4) / 5.3 - 3.4
Vavg = 97.74 - 39.55 / 1.9
Vavg = 30.63 m/s
b) Instantaneous speed
v = dx/dt
v = 3.75*(2t) - 2*1
v = 7.5*t - 2
v(3.4) = 7.5*3.4 - 2
v(3.4) = 23.5 m/s
and
v(5.3) = 7.5*5.3 - 2
v(5.3) = 37.75 m/s
c) average acceleration = delta v / delta T
= 37.75 - 23.5 / 5.3 - 3.4
= 7.5 m/s2
d) instantaneous acceleration , a = dv / dt
a = 3.75*(2) = 7.5 m/s2
a(3.4) = 7.5 m/s2
a(5.3) = 7.5 m/s2
e)
The object is rest at V=dX/dt=0
7.5*t - 2 = 0
t = 0.267 s