a car accelerates uniformly from +10.0m/s to +50.0m/s over a distance of 225 m. How long did it take to go that distance?

Question

anonymous · Answer

@Nnesha

matt101 · Answer

Since the car accelerates uniformly, you can view the car as traveling the ENTIRE time at the average speed. In other words, even though in reality the speed of the car was changing from 10 to 50 m/s, it covers the same distance, in the same time, as if it were going (50+10)/2 = 30 m/s the entire time.

This simplifies the situation so that we can solve in one step. We have a speed (30 m/s) and we have a distance (225 m). We can now easily find time using v=d/t to get t = 7.5 s.

If you didn't realize that you can do the above, you can solve the question using a slightly longer method. You have v(i), v(f), and d, so you can use these values to find the acceleration by:

$$v_{f}^2=v_{i}^2+2ad$$
Solving for a you should get a = 5.33 m/s^2. Then you can use a = [v(f)-v(i)]/t to find t, and by plugging in the numbers you'll still get t = 7.5 s!

Hope that helps!

anonymous · Answer

that helped a lot! I appreciate you taking the time to type all of that and showing me an easier method!!

anonymous · Answer

in the first method what would be v and d? @matt101

matt101 · Answer

"This simplifies the situation so that we can solve in one step. We have a speed (30 m/s) and we have a distance (225 m). We can now easily find time using v=d/t to get t = 7.5 s."