Question

A woman on a bike accelerates from rest at a constant rate for 10 seconds, until the bike is moving at 20m/s. She maintains this speed for 30 seconds, then applies the brakes to decelerate at a constant rate. The bike comes to a stop 5 seconds later.help?

a) what is the bike's acceleration over the last 5 seconds of the journey?
b) how far does the bike travel during this journey?

Thank you!

Answer 1

`"Part a) acceleration "a = -4 m/s^2`
`"Part b) total distance traveled is "750 m`

Explanation:

`v = v_0 + a t`

`"Part a) In the last 5 seconds we have : "`
`0 = 20 + 5 a`
`=> a = -4 m/s^2`

`"Part b)"`
`"In the first 10 seconds we have : "`
`20 = 0 + 10 a`
`=> a = 2 m/s^2`
`x = v_0 t + a t^2 / 2`
`=> x = 0 t + 2 * 10^2 / 2 = 100 m`
`"In the next 30 seconds we have constant velocity : "`
`x = v t => x = 20 * 30 = 600 m`
`"In the last 5 seconds we have : "`
`x = 20 * 5 - 4 * 5^2 / 2 = 50 m`

`=> " Total distance "x = 100 + 600 + 50 = 750 m`

`"Remark : "`
`"20 m/s = 72 km/h, that is very fast"`
`"and this in 10 seconds. That is not possible in reality, the"`
`"woman is a Porsche, LOL !"`