Comparison of Final Speed Between Joe and Jim in a Race

Joe and Jim in a Race: A Comparison of Final Speed

Joe and Jim start at rest at the starting line of a race track. Both runners accelerate at the same rate, but Joe accelerates for twice as long as Jim. Describe the final speed of Joe compared to Jim.

Question:

What is the final speed of Joe compared to Jim in the race?

Answer:

Vf₂ = 2 Vf₁

It shows that the final speed of Joe is twice the final speed of Jim.

Explanation:

First, we analyze the final speed of Jim by using the first equation of motion:

Vf₁ = Vi + at

where,

Vf₁ = final speed of Jim

Vi = initial speed of Jim = 0 m/s

a = acceleration of Jim

t = time of acceleration for Jim

Therefore,

Vf₁ = at ---------------- equation (1)

Now, we see the final speed of Joe. For Joe, the parameters will become:

Vf = Vf₂

Vi = 0 m/s

a = a

t = 2t

Therefore,

Vf₂ = 2at

Using equation (1):

Vf₂ = 2 Vf₁

It shows that the final speed of Joe is twice the final speed of Jim.