What is the speed of a speed skater at the finish line of a downhill course?

In summary, a speed skater starts at a speed of 30m/s and accelerates uniformly for 5 seconds on a 200m downhill course. The question asks for her speed at the finish line, and the solution provided an incorrect answer of 45m/s. Using the correct formula, the final speed is calculated to be 50m/s.
  • #1
jaxreid
2
0

Homework Statement


A speed skater crosses the start line of a straight 200m downhiull course with speed of 30m per second. She accellerated uniformly all the way down taking 5 sec to cover the course - what is her speed at the finish line? I know this should be simple, but just can't get the answer to work out the same as the solution in the paper.


Homework Equations



s = 1/2 (u+v)t

The Attempt at a Solution


200 = 1/2 (30+v)5
200/5 = 1/2(30+v)
40 = 1/2(30+v)
2 x 40 = 30 + v
80 - 30 = v
v = 50m per sec

Answer in book is 45 - HOW?
 
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  • #2
I have to wonder about the answer you are given. According to them the average speed is .5(30+45)=37.5 m/s. That won't cover the 200 m in 5 seconds. I agree with you.

The constant (uniform) acceleration rate is 4 m/s*s gotten from: x = V0*t+.5*a*t^2

Inserting that into Vf = V0 + a*t yields Vf=50 m/s.

So I don't understand either.
 
  • #3
Lawrence - many thanks - was starting to think I'd lost the plot, am glad you agree. The question's from a past paper and the published answer was 45. Just goes to show, they don't always get it right, will point this out to my physics teacher when school returns on Tuesday. Thanks again for your prompt reply.

Jax
 

What is an equation of motion?

An equation of motion is a mathematical representation of the relationship between an object's position, velocity, and acceleration over time. It describes how an object's motion changes with respect to time.

What are the three types of equations of motion?

The three types of equations of motion are the first, second, and third laws of motion, also known as Newton's laws. These laws describe the relationship between an object's motion, the forces acting on it, and its mass.

How do you use equations of motion to solve problems?

To solve problems using equations of motion, you first need to identify the initial and final conditions of the object's motion, such as its initial position, velocity, and acceleration. Then, you can use the appropriate equation of motion to calculate the unknown variable.

What is the difference between linear and rotational equations of motion?

Linear equations of motion deal with the motion of objects in a straight line, while rotational equations of motion deal with the motion of objects around an axis or point. Rotational equations of motion take into account additional factors, such as angular displacement and torque, that are not present in linear equations of motion.

Are equations of motion limited to only one-dimensional motion?

No, equations of motion can be used to describe the motion of objects in both one, two, and three dimensions. For example, the equations of motion for an object moving in a curved path would be different from those for an object moving in a straight line.

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