11. A bicycle takes 8.0 seconds to accelerate at a constant rate from rest to a speed of \( 4.0 \mathrm{~m} / \mathrm{s} \). If the mass of the bicycle and rider together is 85 kg , what is the net force acting on the bicycle? (Hint: first, calculate acceleration)

To find the net force acting on the bicycle, we first need to calculate the acceleration. The formula for acceleration \( a \) is given by the change in velocity (\( \Delta v \)) divided by the time taken (\( t \)). Here, the change in velocity is \( 4.0 \, \mathrm{m/s} - 0 \, \mathrm{m/s} = 4.0 \, \mathrm{m/s} \), and the time taken is \( 8.0 \, \mathrm{s} \). Thus, \[ a = \frac{\Delta v}{t} = \frac{4.0 \, \mathrm{m/s}}{8.0 \, \mathrm{s}} = 0.5 \, \mathrm{m/s^2} \]. Now, we can calculate the net force \( F \) using Newton's second law \( F = ma \), where \( m = 85 \, \mathrm{kg} \) (mass) and \( a = 0.5 \, \mathrm{m/s^2} \) (acceleration): \[ F = 85 \, \mathrm{kg} \times 0.5 \, \mathrm{m/s^2} = 42.5 \, \mathrm{N} \]. Therefore, the net force acting on the bicycle is \( 42.5 \, \mathrm{N} \).