# Difficult kinematics/power question

In summary, the conversation discusses the calculation of average and maximum power for a sprinter who runs a 50 meter dash in 8.5 seconds. The sprinter accelerates at a constant rate for the first second and then runs at a constant velocity for the rest of the race. The formula for average power is total energy expended over time, and the formula for maximum power is force multiplied by velocity. The conversation also mentions using kinematics to solve for the sprinter's velocity, taking into account the acceleration and constant speed over different distances.
1. A sprinter, whose mass is 75 kg, runs a 50 meter dash. The total elapsed time is 8.5 seconds. The sprinter accelerates at a constant rate over the first second and runs the rest of the race at constant velocity.

a. Calculate the average power produced for the first second.
b. What is the maximum power the sprinter generates?

hint: Displacement over the 1st second plus displacement over the rest of the race = 50 meters.

2. Kinematics: D=(v0+v1)/2)*t, P=w/t, P=Fv

3. i tried putting 50=(0+v1)/2)*8.5 to get V, but since there are two diffrent speeds because he accelerates, I don't think this is right. I put 0 for V0, d=5-, and t=1 and tried to solve for A, but to no avail.

Any help would be appricated.

Avg power = total energy expended/time.

If v is the speed at the end of one sec, then (1/2)mv^2 is the total energy spent in 1 s.

Find v from kinematics. Try to figure out the rest.

Ok, for kinematics to solve for V, is 50=((0+V)/2)*8.5 right? Does this give me his constant velocity over the 50m?

I got 11.76 M/S when solving that, that seems a bit too fast...it this correct?

Ok, for kinematics to solve for V, is 50=((0+V)/2)*8.5 right? Does this give me his constant velocity over the 50m?

No. He has not gone at a const v for 50 m, neither he has accelerated for 50 m.

He has accelerated only for the first one second, for a dist of d say, and traveled at the same speed v for the rest 7.5 s over a dist of 50-d. Find the relations between v and d considering accn over the dist d, and again considering const speed over the dist 50-d. Your aim is to find v.

## 1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

## 2. What makes a kinematics/power question difficult?

A kinematics/power question can be difficult if it involves multiple variables, complex equations, or requires a deep understanding of concepts such as acceleration, velocity, and displacement.

## 3. How can I approach a difficult kinematics/power question?

First, identify all given information and variables. Then, choose the appropriate equation(s) to solve for the unknown variable. Finally, plug in the values and solve for the unknown.

## 4. Can I use the same kinematics equations for both linear and rotational motion?

No, kinematics equations for linear motion cannot be directly applied to rotational motion. Different equations and variables are used to describe rotational motion, such as angular velocity and torque.

## 5. How is power related to kinematics?

Power is the rate at which work is done or energy is transferred. In kinematics, power is related to the rate of change of an object's kinetic energy, which is influenced by its velocity and mass.

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