An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is s = 6 cos(t) + 5 sin(t), t ≥ 0, where s is measured in centimeters and t in seconds. (Take the positive direction to be downward.) (a) Find the velocity and acceleration at time t.

V = 1.4m/a

acceleration = - 7.68m/s^2

Step-by-step explanation: The question can be solved by using differential calculus.

Please find the attached file for the solution

Velocity = -7.806 m/s and acceleration = -0.253 m/s²

Step-by-step explanation:

From the question, we know that;

s = 6 cos(t) + 5 sin(t)

Velocity (V(t)) =S'(t) =-6sin(t) + 5cos(t)

Acceleration (a(t)) = V'(t) = - 6cos(t) - 5 sin(t)

A) Hence, we have to solve for s =0;

0 = 6 cos(t) + 5 sin(t)

Thus, 5 sin(t) = - 6 cos(t)

Sin(t) = -(6/5)cos(t)

Sin(t) = - 1.2Cos(t)

Sin(t)/Cos(t) = - 1.2

Tan(t) = - 1.2

t = Tan^(-1)(-1.2)

t = -51.9

But this problem is in radians and thus, converting to radians we get;

t = -51.9 x 0.0175 = - 0.9083 radians

we know t > 0. The first positive solution to tan (t) will be = - 0.9083 + π = - 0.9083 + 3.1416 = 2.2333 seconds

A) Velocity = -6sin(t) + 5cos(t)

Thus, since t = 2.2333 and using radians calculator;

Velocity = -6sin(2.2333) + 5cos(2.2333) = -4.731 - 3.075 = -7.806 m/s

B) Acceleration = -6cos(t) - 5 sin(t)

At t = 2.2333, and using radians calculator

Acceleration = -6cos(2.2333) - 5 sin(2.2333) = 3.689 - 3.942 = -0.253 m/s²

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

alright well the answers to your question is

2xy/9 hope this have a nice day : )

step-by-step explanation: