A basic velocity/distance traveled problem (need work checked)

  • #1

Homework Statement


A car starts from rest and reaches a velocity of 100 km/hr after accelerating uniformly for 10 seconds. how far has the car gone? what is its average velocity?


Homework Equations





The Attempt at a Solution


so since this car accelerates uniformly, i assume that it means it has a constant acceleration, meaning the velocity is a linear equation. converting the final velocity to m/sec, i got 250/9 m/sec.

the slope of this line is then 25/9 (using equation for slope, (y_2-y_1)/(x_2-x_1), plugging in values of 250/9 for final velocity and 0 for initial, 10 for final time and 0 for initial).

then the equation for velocity is then (25/9)t.
so,
distance=integral of (25/9)t from t=0 to t=10, yielding an answer of 1250/9 meters, or about 138.89 meters.

for the second part, i just divide this integral by the difference of the two endpoints of the interval; namely 10 and 0.

avg value = integral of (25/9)t from 0 to 10, divided by 10.
this gives me the average velocity, 13.89 m/sec.

am I on the right track here?
 
Last edited:

Answers and Replies

  • #2
Doc Al
Mentor
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1,247
Looks good to me.
 
  • #3
2,685
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EDIT: already checked, never mind. I personally find the equations of motion simpler for a situation such as this, but if that's how feel more comfortable go for it.

My answers agree with yours and so I'd say it looks good.
 
  • #4
this is true, jarednjames, but i find it a lot simpler to use calculus... just my mindset at least. :P

thanks for the responses!
 

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