during the first 10 seconds? Calculating A car starts from rest and increases its speed to \( 15 \mathrm{~m} / \mathrm{s} \) in 20 seconds. What is the car's acceleration?

To find the car's acceleration, we can use the formula: \[ a = \frac{\Delta v}{\Delta t} \] where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time. The car starts from rest (initial velocity \( v_i = 0 \)) and reaches a final velocity of \( v_f = 15 \mathrm{~m/s} \) in \( \Delta t = 20 \) seconds. So, \[ a = \frac{15 \mathrm{~m/s} - 0}{20 \text{ s}} = \frac{15 \mathrm{~m/s}}{20 \text{ s}} = 0.75 \text{ m/s}^2 \] Thus, the car's acceleration is \( 0.75 \text{ m/s}^2 \). Now, let’s visualize this: In the first 10 seconds, the car has covered half the time of its acceleration period. If it maintains a constant acceleration of \( 0.75 \text{ m/s}^2 \), it will travel a distance of \[ d = \frac{1}{2} a t^2 = \frac{1}{2} (0.75 \text{ m/s}^2)(10 \text{ s})^2 = 37.5 \text{ m} \] So in just 10 seconds, it moves 37.5 meters! How cool is that? If you're looking to see more about the world of acceleration, check out basic physics textbooks or online courses that dive deeper into kinematics. They often have interactive simulations to visualize motion—engaging and you’ll be a physics whiz in no time!