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!

1 Answer
MattyMatty
Apr 22, 2018

#"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 !"#

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