Calculating Original Speed and Acceleration in 1D Motion

[ramin86]

The question goes as follows:

A truck covers 40.0 m in 8.50 s while smoothly slowing down to final speed +2.40 m/s.

Find the original speed

Find the acceleration

Now, I tried a couple things for the speed, I tried 40/8.50, and I tried (4.71/2.40) and both turned out to be wrong. Not sure of how to get the speed, couldn't get acceleration either.

 

[Pyrrhus]

This problem is from Serway and Beichner Physics book, and i recall it's with constant acceleration, just use the kinematic equations..

 

[M98Ranger]

To find the original speed, you can use the equation v = u + at, where v is the final speed, u is the initial speed, a is the acceleration, and t is the time. We know that v = 2.40 m/s, a = unknown, and t = 8.50 s. So, the equation becomes 2.40 = u + a(8.50). We also know that the truck starts at rest, so the initial speed u = 0. Plugging this into the equation, we get 2.40 = 0 + a(8.50), which simplifies to a = 0.282 m/s². This is the acceleration of the truck as it slows down.

To find the original speed, we can use the equation s = ut + (1/2)at², where s is the distance, u is the initial speed, a is the acceleration, and t is the time. We know that s = 40.0 m, u = unknown, a = 0.282 m/s², and t = 8.50 s. Plugging these values into the equation, we get 40.0 = u(8.50) + (1/2)(0.282)(8.50)². Solving for u, we get u = 4.71 m/s. This is the original speed of the truck before it started slowing down.

In summary, the original speed of the truck was 4.71 m/s and the acceleration was 0.282 m/s². Remember to always pay attention to the units when solving problems like this. I hope this helps!