Linear motion: a runner with two accelerations: 1 constant other not

[Genecks]

Homework Statement

Problem 3.7 Suppose that motion studies of a runner show that the maximum speed he
can maintain for a period of about 10 s is 12 m/s. If in a 100-m dash this runner
accelerates with constant acceleration until he reaches this maximum speed and then
maintains this speed for the rest of the race, what acceleration will he require if his total
time is 11 s?

Homework Equations

a = v²/(22v - 200)

The Attempt at a Solution

a = 2.25 m/s²

I've read through the solution. What I don't understand stand, however, is why v here would be the 12 m/s value. Sure, that's the velocity given, but how and why should I know to use 12 m/s? Why do I plug that into the relevant equation? I could say, sure, because it's the only velocity value given, but why that particular value?

 

[mkbowers99]

Well,
Acceleration is based on how much velocity needs to be attained. Velocity itself is determined as distance/time. So either you need to plug in the velocity or the date and time to arrive at an acceleration value!

 

[rl.bhat]

He reaches the maximum velocity in time t₁ with acceleration a. He covers the remaining distance in time (t - t₁) with maximum velocity.
Use the time velocity graph to find the total displacement.
S = 1/2*t₁v_Max + v_max*(t - t₁).
t and v_max is given. Find t₁ ,and hence find acceleration.

 

[CWatters]

linear motion: a runner with two accelerations: 1 constant other not

In case it's not obvious the title is wrong..

The runner first accelerates and then continues at constant velocity.

 

[CWatters]

I've read through the solution. What I don't understand stand, however, is why v here would be the 12 m/s value. Sure, that's the velocity given, but how and why should I know to use 12 m/s? Why do I plug that into the relevant equation? I could say, sure, because it's the only velocity value given, but why that particular value?

Well first assume he's trying to win so he will run at max velocity for as long as possible. It's reasonable to assume that will be done at the end of the race.

So in effect you are being asked to work out how fast he has to accelerate to reach a max velocity. That max velocity is bound to figure in the equations somewhere!

The equations of motion normally need the starting velocity (normally U) and the final velocity (normally V). In this case U=0. V=12m/s.