An object moves along the x axis according to the equation x = 3.20 t 2 2.00 t +
ID: 1879549 • Letter: A
Question
An object moves along the x axis according to the equation
x = 3.20t2 2.00t + 3.00,
where x is in meters and t is in seconds.
1) Determine the average speed between t = 2.10 s and t = 3.40 s
2) Determine the instantaneous speed at t = 2.10 s.
3) Determine the instantaneous speed at t = 3.40 s.
4) Determine the average acceleration between t = 2.10 s and t = 3.40 s.
5) Determine the instantaneous acceleration at t = 2.10 s.
6) Determine the instantaneous acceleration at t = 3.40 s.
7) At what time is the object at rest?
Explanation / Answer
given
x = 3.20t2 2.00t + 3.00
1)
t = 2.10 s t = 3.40 s
at t = 2.1 s
x1 = 3.20 X 2.12 2.00 X 2.1 + 3.00
x1 = 12.912 s
at t = 3.4 s
x2 = 3.20 X 3.42 2.00 X 3.4 + 3.00
x2 = 33.192 s
Vavg = x2 - x1 / dt
= 33.192 - 12.912 / ( 3.4 - 2.1 )
Vavg = 15.6 m/s
2)
at t = 2.1 s
v1 = dx/dt
= 6.4 t - 2
v1 = 11.44 m/s
3 )
t = 3.4 s
v2 = dx/dt
= 6.4 t - 2
v2 = 19.76 m/s
4 )
aavg = v2 - v1 / dt
= 19.76 - 11.44 / ( 3.4 - 2.1 )
aavg = 6.4 m/sec2
5 )
a1 = dv/dt
= 6.4 / 2.1
a1 = 3.047 m/sec2
6 )
a2 = dv/dt
= 6.4 / 3.4
a2 = 1.882 m/sec2
7 )
v = 6.4 t - 2
v = 0
6.4 t = 2
t = 0.3125 sec