Question

A body starts slipping down an incline and moves half metre in half second. How long will it take to move the next half metre?

Answer 1

Let a be the acceleration of the body sliding down. 

From the above diagram:
R − mg cos θ = 0
⇒ R = mg cos θ                      (1)
and
ma + mg sin θ − μR = 0

`=> a = ("mg"(sintheta-mu costheta))/m="g"(sintheta-mu costheta)`

For the first half metre, u = 0, s = 0.5 m and t = 0.5 s.
According to the equation of motion,
        v = u + at
           = 0 + (0.5)4 = 2 m/s
`s=ut+1/2at^2`

`0.5=0+1/2a(0.5)^2`

⇒ a = 4 m/s²
For the next half metre, u = 2 m/s, a = 4 m/s² and s = 0.5.
`=>0.5=2t+(1/2)4t^2`
⇒ 2t² + 2t − 0.5 = 0
⇒ 4t² + 4t − 1 = 0
`=>t=(-4+-sqrt(16+16)(2xx4)`

`=1.656/8=0.2027`

Therefore, the time taken to cover the next half metre is 0.21 s