Distance covered under variable acceleration

In summary, variable acceleration refers to a situation where an object's acceleration changes over time due to changing forces or direction of motion. The distance covered under variable acceleration can be calculated using the equation d = v0t + 1/2at^2, where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration. The initial velocity affects the distance covered, with a greater initial velocity resulting in a greater distance covered. The direction of acceleration also plays a role, as it can either increase or decrease the distance covered depending on whether it is in the same or opposite direction as the initial velocity. The distance covered under variable acceleration can also be negative if the object changes direction and moves in
  • #1
lsmiley
1
0
Is it possible to find the distance covered in a certain time when acceleration depends on velocity, such as an electric-powered vehicle might do??
Acceleration := K*velocity + Const
 
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  • #2
a=Kv+C

a=mv(dv/dx)

mv(dv/dx)=Kv+C

you would need to solve that equation, m,K and C are constants most likely by separation of variables.
 
  • #3
Assuming K and C are constants, you can integrate to find v, then integrate to find x.
In this case, assuming starting from stand still, v=C/K*(exp(K*t)-1)
x = C/K*(exp(K*t)/K-t)
 

1. What is variable acceleration?

Variable acceleration refers to a situation in which an object's acceleration changes over time. This can occur when the object is subject to a changing force or when the direction of the object's motion changes.

2. How is distance covered under variable acceleration calculated?

The distance covered under variable acceleration can be calculated using the equation d = v0t + 1/2at^2, where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration.

3. Does the distance covered under variable acceleration depend on the initial velocity?

Yes, the distance covered under variable acceleration is affected by the initial velocity. A greater initial velocity will result in a greater distance covered, assuming all other factors remain constant.

4. How does the direction of acceleration affect the distance covered under variable acceleration?

The direction of acceleration can greatly impact the distance covered under variable acceleration. If the acceleration is in the same direction as the initial velocity, the distance covered will increase. However, if the acceleration is in the opposite direction, the distance covered may decrease or the object may even come to a stop.

5. Can the distance covered under variable acceleration ever be negative?

Yes, the distance covered under variable acceleration can be negative. This occurs when the object's direction of motion changes and it moves in the opposite direction of its initial velocity. In this case, the distance is considered negative because it is measured in the opposite direction of the object's motion.

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