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.
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?