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.