ExAMPLES A car accelerates uniformly at \( 2 m s^{3} \) for \( 5 s \) From moving at \( 4 \mathrm{~m}^{-1} \) East a) What distance will the air travel in \( 5 s \)

To find the distance traveled by the car during the acceleration, we can use the formula for distance under uniform acceleration: \[ d = v_i t + \frac{1}{2} a t^2 \] where \( v_i = 4 \, \text{m/s} \) (initial velocity), \( a = 2 \, \text{m/s}^2 \) (acceleration), and \( t = 5 \, \text{s} \) (time). Plugging in the values: \[ d = 4 \, \text{m/s} \times 5 \, \text{s} + \frac{1}{2} \times 2 \, \text{m/s}^2 \times (5 \, \text{s})^2 \] \[ d = 20 \, \text{m} + \frac{1}{2} \times 2 \times 25 \] \[ d = 20 \, \text{m} + 25 \, \text{m} = 45 \, \text{m} \] So, the car will travel a distance of \( 45 \, \text{meters} \) to the East in \( 5 \, \text{seconds} \). Now, let’s think about the real-world application of this scenario. When determining stopping distances or acceleration capabilities for vehicles, understanding concepts of uniform acceleration is crucial. It helps engineers design cars that can accelerate safely, making sure they can merge onto highways, avoid obstacles, or improve overall performance. For some curveballs you might encounter, a common mistake could be forgetting to convert units or miscalculating the time or acceleration. Always double-check the parameters; a small oversight can lead you to big errors in distance calculations!