Question

1. how much work must be done to accelerate a 110 kg motorbike and its 60.0 kg rider from 0 to 80 km/h? explain your answer.

Explanation:

Step1: Calculate total mass

The total mass $m$ of the motor - bike and rider is the sum of the mass of the motor - bike and the mass of the rider. So $m = 110\ kg+60.0\ kg=170\ kg$.

Step2: Convert final speed to m/s

The final speed $v = 80\ km/h$. To use in SI units, we convert it: $v=80\times\frac{1000}{3600}\ m/s=\frac{80000}{3600}\ m/s=\frac{200}{9}\ m/s\approx22.22\ m/s$. The initial speed $u = 0\ m/s$.

Step3: Use work - energy theorem

The work - energy theorem states that the work done $W$ on an object is equal to its change in kinetic energy $\Delta K$. The formula for kinetic energy is $K=\frac{1}{2}mv^{2}$. Since the initial kinetic energy $K_{i}=\frac{1}{2}mu^{2}=0$ (because $u = 0$), the work done $W=\Delta K=K_{f}-K_{i}=K_{f}=\frac{1}{2}mv^{2}$.
Substitute $m = 170\ kg$ and $v=\frac{200}{9}\ m/s$ into the formula:

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Answer:

The work done is approximately $41975.3\ J$