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

[Whitishcube]

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?

 

[Doc Al]

Looks good to me.

 

[JaredJames]

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.

 

[Whitishcube]

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

thanks for the responses!

 

[rwisz]

Your approach is correct, but there are a few minor errors in your calculations.

First, the conversion from 100 km/hr to m/sec should be 100,000/3600 = 250/9 m/sec, not 250/9 m/sec.

Second, the equation for velocity should be v = (25/9)t + v0, where v0 is the initial velocity (in this case, 0). So the distance traveled would be the integral of (25/9)t from t=0 to t=10, which gives an answer of 1250/9 meters, or about 138.89 meters, as you correctly calculated.

For the average velocity, you should divide the total distance traveled (1250/9 m) by the total time elapsed (10 seconds), giving an average velocity of 125/9 m/sec, or about 13.89 m/sec.

Overall, you are on the right track and have a good understanding of the concepts involved in solving this problem. Just be sure to double check your calculations and units to avoid any minor errors.