1 Within cells, small organelles containing newly synthesized proteins are transported along microtubules by tiny molecular motors called kinesins. What force does a kinesin molecule need to deliver in order to accelerate an organelle with mass \( 1.00 \times 10^{-17} \mathrm{~kg} \) from 0 to \( 8.70 \mu \mathrm{~m} / \mathrm{s} \) within a time of \( 10.0 \mu \mathrm{~s} \) ? \( \square \mathrm{N} \)

To determine the force required by the kinesin molecule to accelerate the organelle, we first need to calculate the acceleration. We can use the formula: \[ a = \frac{\Delta v}{\Delta t} \] where \( \Delta v = 8.70 \, \mu m/s = 8.70 \times 10^{-6} \, m/s \) and \( \Delta t = 10.0 \, \mu s = 10.0 \times 10^{-6} \, s \). Calculating the acceleration: \[ a = \frac{8.70 \times 10^{-6} \, m/s}{10.0 \times 10^{-6} \, s} = 0.870 \, m/s^2 \] Next, we can find the force using Newton's second law: \[ F = m \cdot a \] where \( m = 1.00 \times 10^{-17} \, kg \). So, \[ F = 1.00 \times 10^{-17} \, kg \times 0.870 \, m/s^2 = 8.70 \times 10^{-18} \, N \] Thus, the force that the kinesin molecule needs to deliver is \( 8.70 \times 10^{-18} \, N \).