Question

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 themagnitude of the accleration of the particle at the instant whenits velocity is zero?
a. 24 m/s²
b. zero
c. 12 m/s²
d. 48 m/s²
e.36 m/s²

Answer 1

First, let's find a velocity function v(t) and accelerationfunction a(t)
then, we'll find a moment when a velocity is zero, and find teacceleration at that moment

We are interested in value of acceleration.
The answer is (a)

Do not forget to rate
Good luck
Vitaly

Answer 2

the simplest way to understand this is that when we look for V(0)

we use the first derivative of x = (24t-2.0t³ ), so we get

0 = 24-6.0t² then solve for T, which we need to get the acceleration

-24 = 6t²

2 = t

now that we have time, we can use the acceleration formula (which is the 2nd derivative of the given function)

a = 12 t.   then we substitudet=2

a = 24m/s^2

x

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