The magnitude of acceleration?

In summary, the magnitude of the acceleration of a particle moving along the x-axis at the instant when its velocity is zero is 24 m/s2. This is determined by finding the derivative of the velocity equation and solving for t, which gives two solutions. However, the negative solution is not physically possible, so the magnitude of the acceleration is 24 m/s2.
  • #1
Ammar w
28
0

Homework Statement


A particle moving along the x-axis has a position given by
x = 24t - 2.0t3 m, where t is
measured in s. What is the magnitude of the acceleration of the particle at the instant
when its velocity is zero?

Homework Equations



v=dx/dt

a=dv/dt=d2x/dt2

The Attempt at a Solution



v = dx/dt = 24 - 6t2 = 0 =>t2 = 4 => t= ± 2

a = dv/dt = d2x/dt2 = -12t

=> a = -12 (2) = -24 m/s2

or a = -12(-2) = 24 m/s2

----------
the right answer is a = 24 m/s2
but why??
 
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  • #2
Time cannot be negative so your second solution, although meaningful in a mathematical sense, can be discarded. But this observation not withstanding, the problem asks for the magnitude of the acceleration.
 
  • #3
PhanthomJay said:
Time cannot be negative so your second solution, although meaningful in a mathematical sense, can be discarded. But this observation not withstanding, the problem asks for the magnitude of the acceleration.

Yes, that's it.
Thank you.
the magnitude is 24 whether time = 2 or -2.
 

1. What is the difference between speed and acceleration?

Speed is the rate at which an object is moving, while acceleration is the rate at which an object's velocity is changing. In other words, acceleration measures how quickly the speed of an object is changing.

2. How is acceleration calculated?

Acceleration is calculated by dividing the change in velocity by the change in time. This can be represented by the formula a = (vf - vi)/t, where "a" is acceleration, "vf" is final velocity, "vi" is initial velocity, and "t" is time.

3. What is the unit of measurement for acceleration?

The SI unit for acceleration is meters per second squared (m/s²). This means that for every second an object is accelerating, its velocity is increasing by 1 meter per second.

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

Acceleration can either increase or decrease an object's velocity, depending on its direction. If an object is accelerating in the same direction as its velocity, its speed will increase. If an object is accelerating in the opposite direction of its velocity, its speed will decrease.

5. What factors can affect the magnitude of acceleration?

The magnitude of acceleration can be affected by various factors, such as the mass of the object, the force applied to the object, and the type of surface the object is moving on. For example, a heavier object will require more force to accelerate at the same rate as a lighter object.

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