Question

Particle travels 10m in 5sec and 10m in 3sec assuming constant acceleration what is the distance travelled in next 2sec? Ans:8.3m

Answer 1

`x = 25/3 = 8.333...`

Explanation:

`v = v_0 + a*t`
`x = v_0 * t + a * t^2/2`
`"Now fill in what we know :"`
`10 = v_{01} * 5 + a * 5^2/2`
`10 = v_{02} * 3 + a * 3^2/2`
`v_{02} = v_{01} + a*5`
`=> 10 = v_{01} * 3 + a * 5 * 3 + a * 3^2/2`
`=> 10 = 3 * v_{01} + 19.5 * a`

`"Now we have a system of two linear equations in 2 variables"`
`v_{01} " and "a.`

`5 v_{01} + 12.5 a = 10`
`3 v_{01} + 19.5 a = 10`

`"Subtract the second equation from the first :"`

`2 v_{01} - 7 a = 0`
`=> v_{01} = 3.5 a`

`=> 10.5 a + 19.5 a = 30 a = 10`
`=> a = 1/3 "m/s²"`
`=> v_{01} = 7/6 "m/s"`

`"Next 2 seconds : "`

`v_0 = v_{03} = v_{02} + a*3 = v_{01} + a*8 = 7/6 + 8/3 = 23/6`

`=> x = (23/6) * 2 + (1/3) * 2^2 / 2 = 23/3 + 2/3 = 25/3 = 8.333`