Question

An object travels back and forth along a straight line. Its velocity, in centimeters per second, is given by the function v(t) = 13 sin (pi/45 t), where t is time in seconds. What is the maximum velocity of the object?

A) 0 cm/s
B) 13 cm/s
C) 26 cm/s
D) 90 cm/s

Answer 1

The maximum velocity of the object, given by the function v(t) = 13 sin (pi/45 t), is 13 cm/s, which corresponds to the amplitude of the sine function.

Step-by-step explanation:

The maximum velocity of an object whose velocity is given by the function v(t) = 13 sin (pi/45 t) can be determined by looking at the amplitude of the sine function. The amplitude is the coefficient in front of the sine function, which in this case is 13. Since the sine function oscillates between -1 and 1, the maximum velocity this object can achieve is when sin(pi/45 t) = 1. Therefore, the maximum velocity of the object is 13 cm/s.