Acceleration Problem: Find Final Magnitude

In summary, the problem describes an automobile starting from rest and accelerating to a final velocity in two stages along a straight road. Each stage takes the same amount of time. In stage 1, the magnitude of the car's acceleration is 3.0m/s^2. The magnitude of the car's velocity at the end of stage 2 is 2.5 times greater than at the end of stage 1. Using this information, we can find the magnitude of the acceleration in stage 2, which is 4.5 m/s^2.
  • #1
mslena79
32
0
1. An automobile starts from rest and accelerates to a final velocity in two stages along a straight road. Each stage occupies the same amount of time. In stage 1, the magnitude of the car's acceleration is 3.0m/s^2. The magnitude of the car's velocity at the end of stage 2 is 2.5 times greater than it is at the end of stage 1. Find the magnitude of the acceleration in stage 2.



2. I'm having some trouble, because it seems like there is missing info. Do I just use the velocities?



3. ((2.5)(3.0m/s^2))-3.0 m/s^2 = 7.5m/s^2 - 3.0m/s^2 = 4.5 m/s^2
 
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  • #2
Let t equal the time that each stage takes... let a2 be the acceleration in the second stage.

What is the velocity at the end of stage 1 in terms of t?

What is the velocity at the end of stage 2 in terms of a2 and t?
 
  • #3
velocity at end of stage 1: v=(3.0m/s^2*t)?
 
  • #4
mslena79 said:
velocity at end of stage 1: v=(3.0m/s^2*t)?

Yup. Now using the variable a2... what's the velocity at the end of stage 2?
 
  • #5
a2=2.5v-v/t
 
  • #6
mslena79 said:
a2=2.5v-v/t

Yup a2 = (2.5v - v)/t ...(you need the parentheses)

Now you can substitute from the previous equation into this one to solve for a2.
 
  • #7
comes out to 4.5 m/s^2 still, right?
 
  • #8
mslena79 said:
comes out to 4.5 m/s^2 still, right?

Yup.
 
  • #9
thanks
 

1. What is acceleration and how is it calculated?

Acceleration is the rate of change of an object's velocity over time. It is calculated by dividing the change in velocity by the change in time, or by taking the derivative of the velocity equation with respect to time.

2. Can acceleration be negative?

Yes, acceleration can be negative. A negative acceleration indicates that the object is slowing down, while a positive acceleration indicates that the object is speeding up.

3. How is the final magnitude of acceleration found?

The final magnitude of acceleration can be found by using the equation a = (vf - vi) / t, where a is acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval.

4. What units are used to measure acceleration?

Acceleration is typically measured in meters per second squared (m/s²) in the metric system, and in feet per second squared (ft/s²) in the imperial system.

5. How does acceleration affect an object's motion?

Acceleration affects an object's motion by changing its speed and/or direction. An increase in acceleration will cause the object to move faster, while a decrease in acceleration will cause the object to slow down. A change in acceleration can also cause a change in direction, as seen in circular motion or when an object changes its velocity.

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