Question

A particle starts from rest and has an acceleration function 5 − 10t m/s2 . (a) What is the velocity function? (b) What is the position function? (c) When is the velocity zero?

Answer 1

Step-by-step explanation:

It is given that,

A particle starts from rest and has an acceleration function as :

`a(t)=(5-10t)\ m/s^2`

(a) Since,
`a=(dv)/(dt)`

v = velocity

`dv=a.dt`

`v=\int(a.dt)`

`v=\int(5-10t)(dt)`

`v=5t-(10t^2)/(2)=5t-5t^2`

(b)
`v=(dx)/(dt)`

x = position

`x=\int v.dt`

`x=\int (5t-5t^2)dt`

`x=(5)/(2)t^2-(5)/(3)t^3`

(c) Velocity function is given by :

`v=5t-5t^2`

`5t-5t^2=0`

t = 1 seconds

So, at t = 1 second the velocity of the particle is zero.