Question

Calculate the time taken for a car to cover a distance of 100m if the initial speed is 10km/h and it has a constant acceleration of 1.5m/s2?

Answer 1

`"9.843 seconds"`

Explanation:

`10 {km}/h = 10/3.6 m/s = 25/9 m/s`
`x = v_0 * t + a * t^2/2`
`=> 100 = (25/9)*t + 1.5*t^2/2`
`"This is a quadratic equation in t, we solve it :"`
`=> 3600 = 100*t + 27*t^2`
`=> 27*t^2 + 100*t - 3600 = 0`
`"discriminant : "100^2 + 3600*4*27 = 398800 = 631.5^2`
`=> t = (-100 pm 631.5)/54`
`"we have to take the solution with the + sign as t > 0."`
`=> t = 531.5/54 = 9.843 s`