Question

The velocity of a particle moving along the x axis is given for 1> 0 by v: = (32.0t - 2.00t^3) m/s,
where t is in s. What is the acceleration of the particle when (after t = 0) it achieves its maximum
displacement in the positive x direction?

Answer 1

The acceleration of the particle when it achieves its maximum displacement in the positive x-direction is 32 m/s²

To calculate the acceleration of the particle, we need to differentiate the expression for the velocity.

 

Given:

• v = 32t-2t³

differentiate v with respect to t

• dv/dt = a = 32+2(3)t²
• dv/dt = 32+6t²................... Equation 1

When the particle achieves its maximum displacement,

• t = 0 s

Substitute these value of t into equation 1

• dv/dt = 32+6(0²)
• dv/dt = 32 m/s²

Hence The acceleration of the particle when it achieves its maximum displacement in the positive x-direction is 32 m/s²

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