Graph the equation v = at + v₀ over the domain of 0 < t > 4 hours where a= 10 mph² and v₀= 100 mph.

1. What does the velocity intercept represent? The initial velocity of 100 mph.
   
   
2. Calculate the slope of the graph. 10 mph²
   
   
3. What does the slope represent? Acceleration.
   
   
4. What is your velocity after four hours?140 mph
   Does this make sense?Yes
   
   
5. What happens to your graph if v₀ = 0? The entire graph (straight line) shifts downward to a parallel line whose velocity intercept is zero.
   
   
6. What effect does a change in acceleration a have upon your graph? It changes the slope.
   
   
7. Using the equation x = 1/2 at² + v₀t + x₀ with an x₀ =50 miles, graph x over the domain of 0 < t > 4 hours.
   
   Is this a reasonable domain for this equation? The force will not remain constant for an appreciable time because lift and drag depend upon the square of the velocity. Although our acceleration is relatively small, we are changing the velocity a significant amount in four hours so we probably have assumed too large a domain.