1. ## velocity

Hi there every1,

i have a technology maths question that i am not sure how to solve, if any one knows the solution to this question please let me know, will really appreciate it.

The linear displacement of a component is given by

s=82t – 2t^3

a. Find the velocity v = ds/dt
b. at what value of t is v = 0 ?

2. Well the question is elementary.

ds/dt is the velocity. The derivative of s with respect to t.

Just differentiate the given equation.

so ds/dt= 82- 6t^2

now for v=0, just set the above equation =0 and solve for t..

3. When you have the distance as a function of time, as you have here, the velocity is given by the derivative of the function.

$s(t)=82t-2t^{3}$

To find $\frac{ds}{dt}=v(t)$ , you need to know some basic differentiation rules.

$v(t)=82-6t^{2}$

To find the t for which the velocity is zero, you need to solve a equation in $t$ .

$82-6t^{2}=0$

$t^{2}=\frac{82}{6}$

$t=\sqrt{\frac{41}{3}}$