# Thread: Finding Formula for Velocity

1. ## Finding Formula for Velocity

I have a word problem stating a jet needs a speed of 200 mph to take off
if it can accerlate from 0 to 200 mph in 30 seconds

how long must the runway be (assume assume constant acceleration)

How would I find a proper formula for velocity

2. Assuming Constant acceleration a(t) = 20/3

Integrate to find velocity

then v(t) = 20/3 t since the initial velocity is 0 this is the velocity.

Integrate to find position (in this case same as distance)

d(t) = 10/3 t^2

d(30) = 3000

3. how did you get 20/3

4. 20/3 won't really work because the time units are different; $\displaystyle a(t)=\frac{20}{3}\frac{mi}{hr\cdot s}$. You'll have to convert it to $\displaystyle \frac{mi}{s^{2}}$, $\displaystyle \frac{mi}{hr^{2}}$ or some other units that you'll feel most comfortable with.

5. Originally Posted by sk8erboyla2004
how did you get 20/3
Well, think of acceleration as the slope of the velocity graph, or in other words, the change in velocity over the change in time. He did: $\displaystyle \frac{200 mph - 0 mph}{30 s - 0 s}=\frac{20 mph}{3 s}=\frac{20}{3}\frac{mi}{hr\cdot s}$

6. argh !!! mixed units was thinking 200/30

200mph = 293.3ft/sec

it shoud be 293.3/30 = 9.78

v(t) = .978 t

then d(t) = .489*t^2

d(30) = 440 ft