Time for a cyclist to stop moving if he stops pedalling

[bathmecheng]

Homework Statement

If the rider stops pedalling calculate the distance traveled by the bicycle before it comes to rest from an initial speed of 2m/s.

Mass of rider: 60kg
Mass of bicycle: 7 kg
Drag: 7.5 V^2 (where V is the velocity)
Slope : 10°

The Attempt at a Solution

F= ma
-7.5V^(2) - sin10° mg = ma to find the deceleration

however I know that the drag decreases with the decrease in velocity, hence the deceleration is not constant! I think I should use some sort of integral! HELP!sorry guys I found the formula I was looking for derived by my lecturer!

 

[Valkarie]

x(t) = xo + v0t - (7.5/m)* (V2-V20) + (m*g/7.5)*ln(V/V0)where m= mass of the system, V0 = initial velocity, V = final velocity. so since V= 0 at the end x(t) = xo + v0t - (7.5/m)* (V2-V20) + (m*g/7.5)*ln(V/V0)x(t) = xo + 2t - (7.5/67)* (0-22) + (67*9.8/7.5)*ln(0/2) x(t)= xo + 2t - 3.77 + 4.63 x(t) = xo + 6.4 t since xo = 0 x(t)= 6.4 t distance travelled = 6.4 * time taken to come to rest