\( \begin{array}{l}\text { Mubarak pushes a } 10 \mathrm{~kg} \text { cart } 10 \mathrm{~m} \text { across a floor with a horizontal force of } 80 \mathrm{~N} \\ \text { Calculate the amount of work done by Mubarak on the cart and calculate his } \\ \text { power if he is moving it at } 0.5 \mathrm{~m} / \mathrm{s} \text {. } \\ \qquad W=100 \mathrm{~J}, P=20 \mathrm{~W} \\ W=80 \mathrm{~J}, P=700 \mathrm{~W}\end{array} \) \( \begin{array}{l}\text { W } \mathrm{W}=800 \mathrm{~J}, P=40 \mathrm{~W} \\ \mathrm{~W}=400 \mathrm{~J}, P=400 \mathrm{~W}\end{array} \)

To solve the problem, we need to calculate the work done by Mubarak on the cart and then determine his power based on the speed at which he is moving the cart. ### Step 1: Calculate the Work Done (W) The work done by a force is calculated using the formula: \[ W = F \cdot d \cdot \cos(\theta) \] Where: - \( W \) is the work done, - \( F \) is the force applied, - \( d \) is the distance moved in the direction of the force, - \( \theta \) is the angle between the force and the direction of motion. In this case: - \( F = 80 \, \text{N} \) (the horizontal force applied), - \( d = 10 \, \text{m} \) (the distance moved), - \( \theta = 0^\circ \) (since the force is applied horizontally in the direction of motion). Since \( \cos(0^\circ) = 1 \), the formula simplifies to: \[ W = F \cdot d \] Now substituting the values: \[ W = 80 \, \text{N} \cdot 10 \, \text{m} = 800 \, \text{J} \] ### Step 2: Calculate the Power (P) Power is defined as the rate at which work is done, calculated using the formula: \[ P = \frac{W}{t} \] Where: - \( P \) is the power, - \( W \) is the work done, - \( t \) is the time taken. To find the time taken, we can use the formula: \[ t = \frac{d}{v} \] Where: - \( d = 10 \, \text{m} \) (the distance), - \( v = 0.5 \, \text{m/s} \) (the speed). Calculating the time: \[ t = \frac{10 \, \text{m}}{0.5 \, \text{m/s}} = 20 \, \text{s} \] Now substituting the values into the power formula: \[ P = \frac{800 \, \text{J}}{20 \, \text{s}} = 40 \, \text{W} \] ### Final Results - The work done by Mubarak on the cart is \( W = 800 \, \text{J} \). - The power exerted by Mubarak while moving the cart is \( P = 40 \, \text{W} \). Thus, the correct answer is: - \( W = 800 \, \text{J}, P = 40 \, \text{W} \)