Question

The acceleration of an object (in m/s2) is given by the function a ( t ) = 5sin ( t ) . The initial velocity of the object is v ( 0 ) = − 3 m/s. Round your answers to four decimal places.

Answer 1

The acceleration of an object is given by the function a(t) = 5sin(t). The initial velocity of the object is v(0) = -3 m/s. To find the velocity function, we need to integrate the acceleration function and use the initial velocity value.

Step-by-step explanation:

The acceleration of an object is given by the function a(t) = 5sin(t). To find the initial velocity of the object, we need to find v(0). Using the given information, we have v(0) = 5.0 m/s. Since the derivative of velocity with respect to time is equal to acceleration, we can integrate the acceleration function to find the velocity function. Integrating a(t) = 5sin(t) with respect to t gives us v(t) = -5cos(t) + C. Substituting v(0) = 5.0 m/s into the velocity function gives us C = 5.0 m/s. Therefore, the velocity function is v(t) = -5cos(t) + 5.0 m/s.