An air-track glider is attached to a spring on a frictionless horizontal surface. The air-track glider is pulled to the right and released from rest at t = 0 s. If the air-track glider reaches a maximum speed of 43.9 cm/s and oscillates with a period of 2.50 s, what is the air-track glider's acceleration at t = 0.950 s?a. 80.6 cm/s2b. -46.2 cm/s2c. -4.32 cm/s2d. 14.1 cm/s2

Question
Asked Dec 2, 2019

An air-track glider is attached to a spring on a frictionless horizontal surface. The air-track glider is pulled to the right and released from rest at t = 0 s. If the air-track glider reaches a maximum speed of 43.9 cm/s and oscillates with a period of 2.50 s, what is the air-track glider's acceleration at t = 0.950 s?


a. 80.6 cm/s2
b. -46.2 cm/s2
c. -4.32 cm/s2
d. 14.1 cm/s2

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Expert Answer

Step 1
Given that the maximum speed is v
43.9cm/s
max
and time period is T = 2.50s.
The expression for angular velocity is given by
27T
т
2(3.14)
2.50s
2.512rad/s
The expression for maximum velocity is given by
V
Ao
max
V
A=
max
43.9 cm/s
A=
2.512rad/s
A=17.47 cm
[2]
The expression for acceleration is given by
a(t)-Acosor
Use equation equation [1and [2]in [3].
a(t)(2.512rad/s) (17.47cm)cos[2.512rad/s x 0.950s
a(t) 80.26 cm/s
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Given that the maximum speed is v 43.9cm/s max and time period is T = 2.50s. The expression for angular velocity is given by 27T т 2(3.14) 2.50s 2.512rad/s The expression for maximum velocity is given by V Ao max V A= max 43.9 cm/s A= 2.512rad/s A=17.47 cm [2] The expression for acceleration is given by a(t)-Acosor Use equation equation [1and [2]in [3]. a(t)(2.512rad/s) (17.47cm)cos[2.512rad/s x 0.950s a(t) 80.26 cm/s

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