Question

A shark swimming in the ocean sees a passing fish swimming by and accelerates at 2.2 m/s² to a speed of 23 m/s to overtake it, doing so in 3.2 seconds. What was the shark’s initial speed?

Answer 1

Using the kinematic equation, the shark's initial speed was calculated to be approximately 15.96 m/s, based on its acceleration and the time it took to reach a final speed of 23 m/s.

Step-by-step explanation:

To find the shark’s initial speed, we use the kinematic equation that relates initial velocity (ω), final velocity (υ), acceleration (α), and time (τ): υ = ω + ατ. In this case, the final velocity (υ) is 23 m/s, the acceleration (α) is 2.2 m/s², and the time (τ) is 3.2 seconds. We rearrange the equation to solve for the initial velocity (ω): ω = υ - ατ.

Given that vf = 23 m/s, a = 2.2 m/s², and t = 3.2 s, we can rearrange the equation to solve for vi:

vi = vf - at

Substituting the given values:

vi = 23 m/s - (2.2 m/s²)(3.2 s)

Simplifying:

vi = 23 m/s - 7.04 m/s

Therefore, the shark's initial speed was approximately 15.96 m/s.

Substituting the values, we get: ω = 23 m/s - (2.2 m/s² × 3.2 s) = 23 m/s - 7.04 m/s = 15.96 m/s. Therefore, the shark's initial speed was approximately 15.96 m/s.