We need to apply the following expression
Vf = Vo + a.t
Where a is the acceleration
t is the time it takes to achieve Speed Vf
And Vo the initial speed
In this problem Vo = 60 miles/hour
Vf = 0 (comes to a stop)
t = 4 seconds
a = -60 [miles/hours] / 4 [s] = -15 miles/hour/second (negative as it goes in the opposite direction)
Answer:
a) 
b) 
c) 
Explanation:
a) In the equilibrium position of the system, that is when the spring is not elongated, the potential energy is zero. Therefore, the total energy of the system is the maximum kinetic energy:

b) The force constant of the spring can be calculated from the natural frequency of the system:

Recall that
, that is the distance traveled in one revolution divided into the time of one revolution. Replacing and solving for k:

c) The maximum speed is directly proportional to the amplitude of the motion:

Answer:
a. The horizontal component of acceleration a₁ = 0.68 m/s²
The vertical component of acceleration a₂ = -0.11 m/s²
b. -9.19° = 350.81° from the the positive x-axis
Explanation:
The initial velocity v₁ of the fish is v₁ = 4.00i + 1.00j m/s. Its final velocity after accelerating for t = 19.0 s is v₂ = 17.0i - 1.00j m/s
a. The acceleration a = (v₂ - v₁)/t = [17.0i - 1.00j - (4.00i + 1.00j)]/19 = [(17.0 -4.0)i - (-1.0 -1.0)j]/19 = (13.0i - 2.0j)/19 = 0.68i - 0.11j m/s²
The horizontal component of acceleration a₁ = 0.68 m/s²
The vertical component of acceleration a₂ = -0.11 m/s²
b. The direction of the acceleration relative to the unit vector i,
tanθ = a₂/a₁ = -0.11/0.68 = -0.1618
θ = tan⁻¹(-0.1618) = -9.19° ⇒ 360 + (-9.19) = 350.81° from the the positive x-axis