Question

The velocity of a particle along the s-axis is given by v = 14s^7/6 where s is in millimeters and v is in millimeters per second. Determine the acceleration when s is 5.5 millimeters.

Answer 1

The acceleration is
`2220.00m/s^(2)`

Step-by-step explanation:

We know that the acceleration is given by

`a=v(dv)/(ds)........................(i)`

The velocity as a function of position is given by
`v=14\cdot s^(7/6)`

Thus the acceleration as obtained from equation 'i' becomes

`a=14\cdot s^(7/6)* (d)/(ds)(14\cdot s^(7/6))\\\\a=14\cdot s^(7/6)* (7)/(6)* 14\cdot s^(1/6)\\\\a=(686)/(3)\cdot s^(8/6)`

Hence acceleration at s = 5.5 equals

`a(5.5)=(686)/(3)* (5.5)^(8/6)\\\\\therefore a=2220.00mm/s^(2)`