physics : class11 Velocity-Time Function : Periodic Functions : Oscillations and Waves MCQ Questions and Answers
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Velocity-Time Function
MCQ questions and answers.
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MCQ Questions
1. For a particle executing simple harmonic motion, the velocity-time function is v = Vmax cos(ωt). What is the maximum speed of the particle?
A.
0
B.
Vmax
C.
ωVmax
D.
Vmax/ω
Correct Answer:
Vmax
Explanation:
In the velocity-time function v = Vmax cos(ωt), the cosine factor varies between -1 and +1. Therefore, the greatest magnitude of velocity, or maximum speed, is Vmax.
2. The velocity-time function of a particle is v = 4 sin(2πt) m/s. What is the time period of the velocity function?
A.
0.25 s
B.
0.5 s
C.
1 s
D.
2 s
Correct Answer:
1 s
Explanation:
Comparing with v = Vmax sin(ωt), the angular frequency is 2π rad/s. The time period is T = 2π/ω = 2π/(2π) = 1 s.
3. For the velocity function v = 6 cos(πt) m/s, what is the maximum speed?
A.
π m/s
B.
3 m/s
C.
6 m/s
D.
12 m/s
Correct Answer:
6 m/s
Explanation:
The coefficient of the cosine term gives the amplitude of the velocity function. Hence, the maximum speed is 6 m/s.
4. At what values of ωt is the velocity zero for the function v = Vmax sin(ωt)?
A.
0, π, 2π, ...
B.
π/2, 3π/2, ...
C.
π/4, 3π/4, ...
D.
Only at π/2
Correct Answer:
0, π, 2π, ...
Explanation:
The velocity is zero when sin(ωt) = 0. This occurs at ωt = 0, π, 2π, and other integral multiples of π.
5. If a velocity-time function is v = 5 sin(4t) m/s, what is its angular frequency?
A.
1 rad/s
B.
4 rad/s
C.
5 rad/s
D.
20 rad/s
Correct Answer:
4 rad/s
Explanation:
In the standard form v = Vmax sin(ωt), the coefficient of t is the angular frequency. Therefore, ω = 4 rad/s.
6. For v = Vmax cos(ωt), what is the velocity at t = 0?
A.
0
B.
Vmax
C.
-Vmax
D.
ωVmax
Correct Answer:
Vmax
Explanation:
At t = 0, v = Vmax cos(0) = Vmax because cos(0) = 1.
7. A periodic velocity-time function has a time period of 2 s. What is its frequency?
A.
0.25 Hz
B.
0.5 Hz
C.
1 Hz
D.
2 Hz
Correct Answer:
0.5 Hz
Explanation:
Frequency and time period are related by f = 1/T. Thus, f = 1/2 = 0.5 Hz.
8. For the velocity function v = 3 sin(πt/2) m/s, what is the maximum negative velocity?
A.
0 m/s
B.
-1.5 m/s
C.
-3 m/s
D.
3 m/s
Correct Answer:
-3 m/s
Explanation:
Since the sine function can have a minimum value of -1, the minimum velocity is -Vmax = -3 m/s.
9. Which function represents a velocity that repeats itself after a time period T?
A.
v = Vmax sin(2πt/T)
B.
v = Vmax t
C.
v = Vmax/t
D.
v = Vmax + t
Correct Answer:
v = Vmax sin(2πt/T)
Explanation:
The sine function repeats after its argument increases by 2π. In v = Vmax sin(2πt/T), this occurs when time increases by T, so the velocity is periodic with time period T.
10. The velocity-time function is v = 8 cos(2πt) m/s. What is the velocity at t = 0.5 s?
A.
8 m/s
B.
4 m/s
C.
0 m/s
D.
-8 m/s
Correct Answer:
-8 m/s
Explanation:
Substituting t = 0.5 s gives v = 8 cos(2π × 0.5) = 8 cos(π) = 8(-1) = -8 m/s.
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