Calculate the magnitude of particle acceleration

In summary, the magnitude of the acceleration of a particle at time t=15 seconds can be calculated by finding the second derivative of its position, which is given by r=42t^2i + 41t^3j + 6k. The correct answer is 3691, but the attempted solution resulted in 3774 due to not considering the vector nature of acceleration. The correct acceleration is 246tj + 84i.
  • #1
inflames829
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Homework Statement



A particles position is given by r=42t^2i + 41t^3j + 6k. Calculate the magnitude of its acceleration at time t = 15 seconds

Homework Equations





The Attempt at a Solution



to find the acceleration i found the second derivative which i had as 246t + 84. Then i put 15 in as t and got 3774, but according to the answers i should get 3691. What did i do wrong
 
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  • #2
You are dealing with vectors. The acceleration is 246tj + 84i, not just 246t + 84.
 
  • #3
but do i still have to find the second derivative using this? Can you give me a hint on how to do this?
 
  • #4
ive worked this one out. Thanks for the hint
 

1. What is the formula for calculating particle acceleration?

The formula for calculating particle acceleration is a = Δv/Δt, where a is acceleration, Δv is the change in velocity, and Δt is the change in time.

2. How do you determine the direction of particle acceleration?

The direction of particle acceleration is determined by the direction of the change in velocity. If the velocity is increasing, the acceleration is in the same direction. If the velocity is decreasing, the acceleration is in the opposite direction.

3. What is the unit of measurement for particle acceleration?

The unit of measurement for particle acceleration is meters per second squared (m/s²).

4. What factors affect the magnitude of particle acceleration?

The magnitude of particle acceleration is affected by the force applied to the particle, the mass of the particle, and the resistance or friction present in the environment.

5. Can the magnitude of particle acceleration be negative?

Yes, the magnitude of particle acceleration can be negative if the particle is decelerating or if the acceleration is in the opposite direction of the velocity.

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