9 The graph shows the velocity, in cms-1, of a particle moving along the x-axis from t=0 s to t = 7s. At t=0 the particle is 2 cm to the left of the origin. velocity (cm s 1) 1 time (s) 0 1.5 4.5 7.5 a Find the particle's position at the end of the 7 s. b Find the total distance the particle travelled in the seven seconds.
Answers
Answer:
The period of the oscillation is
T=
f
1
=
1.50 Hz
1
=
(3/2 s
−1
)
1
=
3
2
(a) At t=0,x=0 and v is positive (to the right). Therefore, this situation corresponds to x=Asinωt and v=v
i
cosωt. Since f=1.50 Hz,ω=2πf=3.00π, and A=2.00 cm:
x=2.00cos(3.00πt−90
∘
)=2.00sin3.00πt
where x is in centimeters and t is in seconds.
(b) v
max
=v
i
=Aω=2.00(3.00π)=6.00π cm/s=
18.8 cm/s
(c) The particle has this speed at t=0 and next after half a period:
t=
2
T
=
3
1
s
(d) a
max
=Aω
2
=2.00(3.00π)
2
=18.0π
2
cm/s
2
=
178 cm/s
2
(e) This positive value of maximum acceleration first occurs when the particle is reversing its direction on the negative x axis, three-quarters of a period after t=0: at t=
4
3
T=
0.500 s
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Step-by-step explanation:
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