Question

The displacement (in meters) of a particle moving in a straight line is given by the equation of motion

s = 9/t2,
where t is measured in seconds. Find the velocity of the particle at times

t = a, t = 1, t = 2, and t = 3.

t = a v =___________ m/s
t = 1 v =___________ m/s
t = 2 v =___________ m/s
t = 3 v =___________ m/s

Answer 1

Explanation:

the displacement of the particle is given by

`s=(9)/(t^(2))`

The rate of change of position gives the value of velocity.

So, v = ds/dt

Differentiate the position function with respect to time.

`v = ds/dt=9(-2)t^(-3)=-18t^(-3)`

Now, at t = a

v = -18/a³ m/s

At t = 1

v = - 18 m/s

At t = 2

v = - 18 / 8 = - 2.25 m/s

At t = 3

v = - 18 / 27 = 0.67 m/s