Simple physics problem worries me

[Robert Jan]

This is a basic physics question off an earlier version of an entry exam that I will have to pass for my life to have any meaning. The test has questions on biology, math, chemistry and physics. This is the first physics question, the warm-up. and either I cant even do that or there is a mistake.

I'm concerned that the correct answer is not provided in the multiple choice.

A sprinter has to run 100 meter.

During the first 1.250 seconds, he constantly accelerates with 8.0 meters per second^2.

After that his speed remains constant until the finish.

How long does he take to run the 100 meters?


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My answer was he accelerates by 8.0 meters per second^2 for 1.250 seconds, so after 1.250 seconds he is moving at 10 meters per second.

his average speed during the first 1.250 seconds is 4.0 meters per second.
so after 1.250 seconds he has travelled 5 meters, and has 95 meters to go.

He does these 95 meters with 10 meters/second, so it takes him 9.5 seconds.

Therefor the total time it takes him to travel the 100 meters, =
9.5 + 1.250 = 10.75 seconds.

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However the answers to choose from are
A> 10.000 s
B> 10.250 s
C> 10.455 s
D> 10.625 s

And the answer model says answer D is correct.
Did I make a mistake?
or
Is there really a mistake in such an important test?
Both would be rediculous.

 

[Sigmund Roid]

x1=1/2*a*t1^2=4*1.25^2=6.25 m
v2=a*t1=8*1.25=10 m/s
x2=100-x1=93.75 m
t2=x2/v2=9.375 s
t=t1+t2==10.625 s = (D)
piece a cake

 

[Sigmund Roid]

The average of an arbitrary function is actually <y>=1/(t2-t1)*int(y(t)dt)(t1..t2)
only for linear functions that is equal to (y(t2)-y(t1))/(t2-t1)

 

[gonelifting]

"My answer was he accelerates by 8.0 meters per second^2 for 1.250 seconds, so after 1.250 seconds he is moving at 10 meters per second. "



He moved 10 meters at this point but not 10 meters per second. He`s still moving 8 meters per second.

 

[Robert Jan]

Of course!
thanks

This is due to the problems in HS having such simple numbers I tell you.

The acceleration is 8.0. but the speed reached with it is 10.0.

so the average speed during constant acceleraion is 5.0, not 4.0.

Just a slip. but a dangerous one because I made it twice.

 

[Robert Jan]

"My answer was he accelerates by 8.0 meters per second^2 for 1.250 seconds, so after 1.250 seconds he is moving at 10 meters per second. "



He moved 10 meters at this point but not 10 meters per second. He`s still moving 8 meters per second.

you are wrong. you're mistaking acceleration for speed.

 

[gonelifting]

you are wrong. you're mistaking acceleration for speed.

thanks.

 

[vinylgroover]

thanks.

lol