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

## 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?

## 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?

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Looks good to me.

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.

this is true, jarednjames, but i find it a lot simpler to use calculus... just my mindset at least. :P

thanks for the responses!