An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.00m/s2. Find the final speed and the displacement after 5 s

To find the final speed and the displacement of the automobile after 5 seconds, we can use the following kinematic equations: 1. **Final velocity \( v \)**: \[ v = u + a t \] where: \( u \) = initial speed (4.30 m/s) \( a \) = acceleration (3.00 m/s²) \( t \) = time (5 s) 2. **Displacement \( s \)**: \[ s = ut + \frac{1}{2} a t^2 \] Now, let's calculate the final speed: ### Calculation of Final Speed \[ v = 4.30 \, \text{m/s} + (3.00 \, \text{m/s}^2 \times 5 \, \text{s}) \] \[ v = 4.30 \, \text{m/s} + 15.00 \, \text{m/s} \] \[ v = 19.30 \, \text{m/s} \] ### Calculation of Displacement \[ s = (4.30 \, \text{m/s} \times 5 \, \text{s}) + \frac{1}{2} (3.00 \, \text{m/s}^2 \times (5 \, \text{s})^2) \] \[ s = (21.50 \, \text{m}) + \frac{1}{2} (3.00 \, \text{m/s}^2 \times 25 \, \text{s}^2) \] \[ s = 21.50 \, \text{m} + \frac{1}{2} (75.00 \, \text{m}) \] \[ s = 21.50 \, \text{m} + 37.50 \, \text{m} = 59.00 \, \text{m} \] ### Summary of Results - **Final Speed**: \( 19.30 \, \text{m/s} \) - **Displacement**: \( 59.00 \, \text{m} \)