11. A spider accelerates from a standstill to \( 5 \mathrm{~m} / \mathrm{s} \) in 10 s . What is it's acceleration? 12. An ant carries food at \( 2 \mathrm{~cm} / \mathrm{s} \). How long will it take an ant to carry a cookie crumb 200 cm ? 13. If you leave for a trip at 8 am and arrive at 4 pm , the velocity was 55 mph north, how far did you drive?

Sure, let's tackle each of these problems one by one. --- ### **Problem 11** **A spider accelerates from a standstill to \( 5 \, \text{m/s} \) in 10 seconds. What is its acceleration?** **Solution:** Acceleration (\( a \)) is defined as the change in velocity (\( \Delta v \)) divided by the time (\( t \)) taken for that change. The formula for acceleration is: \[ a = \frac{\Delta v}{t} \] - **Initial velocity (\( u \))**: \( 0 \, \text{m/s} \) (since it starts from rest) - **Final velocity (\( v \))**: \( 5 \, \text{m/s} \) - **Time (\( t \))**: \( 10 \, \text{s} \) Plugging in the values: \[ a = \frac{5 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = \frac{5 \, \text{m/s}}{10 \, \text{s}} = 0.5 \, \text{m/s}^2 \] **Answer:** The spider's acceleration is **\( 0.5 \, \text{m/s}^2 \)**. --- ### **Problem 12** **An ant carries food at \( 2 \, \text{cm/s} \). How long will it take an ant to carry a cookie crumb \( 200 \, \text{cm} \)?** **Solution:** Time (\( t \)) can be calculated using the formula: \[ t = \frac{\text{Distance}}{\text{Speed}} \] - **Distance (\( d \))**: \( 200 \, \text{cm} \) - **Speed (\( v \))**: \( 2 \, \text{cm/s} \) Plugging in the values: \[ t = \frac{200 \, \text{cm}}{2 \, \text{cm/s}} = 100 \, \text{seconds} \] **Answer:** It will take the ant **100 seconds** to carry the cookie crumb. --- ### **Problem 13** **If you leave for a trip at 8 am and arrive at 4 pm, traveling at a velocity of 55 mph north, how far did you drive?** **Solution:** First, determine the total time of the trip. - **Departure time:** 8 am - **Arrival time:** 4 pm Total time (\( t \)): \[ 4 \, \text{pm} - 8 \, \text{am} = 8 \, \text{hours} \] Next, use the formula for distance (\( d \)): \[ d = \text{Velocity} \times \text{Time} \] - **Velocity (\( v \))**: \( 55 \, \text{mph} \) - **Time (\( t \))**: \( 8 \, \text{hours} \) Plugging in the values: \[ d = 55 \, \text{mph} \times 8 \, \text{hours} = 440 \, \text{miles} \] **Answer:** You drove a total distance of **440 miles** north. --- If you have any more questions or need further clarification on these problems, feel free to ask!