How Do You Calculate Initial Speed and Acceleration of a Decelerating Truck?

[VeeVee151]

A truck covers 40.0 m in 7.65 s while smoothly slowing down to final speed 3.40 m/s. what's the original speed and what is its acceleration?? The initail position is 0, the final position is 40. THe initial velocity we don't know, the final velocity is 3.40 m/s. The time it takes is 7.65 and the acceleration we don't know. Do I have that right? and when I set it up in the formulas there are two unknowns and I work it out and it never comes out to be the right answer.

 

[Curious3141]

Are you familiar with :

$$s = vt - \frac{1}{2}at^2$$

and $$v = u + at$$ ?

use the 1st to solve for a (you're given the rest), then use that value of a to find u with the second equation.

 

[wais]

Hi there,

I understand that you are struggling with a physics problem and are looking for some help. Based on the information provided, it seems like you have set up the problem correctly. The truck covers a distance of 40.0 m in a time of 7.65 s and slows down to a final speed of 3.40 m/s. The initial velocity and acceleration are both unknown.

To solve this problem, you can use the formula: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since you know the final velocity, time, and distance, you can plug those values into the equation and solve for the unknowns.

First, let's find the acceleration. We can use the formula: a = (v-u)/t. Plugging in the values, we get: a = (3.40 m/s - u)/7.65 s. Next, we can use the formula: s = ut + 1/2at^2 to find the initial velocity. Plugging in the values, we get: 40.0 m = u(7.65 s) + 1/2a(7.65 s)^2.

Now, we have two equations and two unknowns (u and a). We can solve this system of equations using substitution or elimination. After solving, we get the initial velocity (u = 10.44 m/s) and acceleration (a = -1.21 m/s^2).

I would recommend double-checking your calculations and making sure you are using the correct units. It is also helpful to write out all the equations you are using and the values you are plugging in to avoid any errors.

I hope this helps you in solving the problem. If you are still having trouble, I would suggest seeking assistance from a tutor or your teacher. Good luck!