Question

Starting at time t = 0, an object moves along a straight line. Its coordinate in meters
is given by x(t) = 75t - 1.0t3 , where t is in s. When velocity (v) of the object = 0, the
value of its acceleration is : (Ans: -30 m/s2 )

Answer 1

Answer:

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Answer 2

Answer: When velocity (v) of the object = 0, the

value of its acceleration is - 30 m/s²

Explanation:

Given the equation of the motion of the particle :

x(t) = 75t - 1.0t³ ------------------(1)

Differentiating the equation (1) with respect to t will give us the velocity of the particle in terms of t.

$\frac{d}{dt}$  x(t) = 75 - 3t²

=> v(t) = 75 - 3t² ----------------------(2)

Where v(t) = velocity of the particle in terms of t.

v(t) = 0

=> 75 - 3t² = 0

=> t = $\sqrt{\frac{75}{3} }$ = 5 sec

So, the velocity of the particle is zero at t = 5 sec.

Now, differentiating the equation (2) with respect to t will give us the acceleration of the particle in terms of t.

a(t) = $\frac{d}{dt}$  v(t) = -6t -----------------------------(3)

Where, a(t) is the acceleration of the particle in terms of t.

Now, the acceleration of the particle at t = 5 sec is:

a(5) = -6 . 5 = - 30 m/s²

So, the acceleration of the particle when its velocity is zero is - 30 m/s²