To determine the velocity of a car that accelerates from rest at a rate of 3 m/s² after 5 seconds, we can use the basic kinematic equation for linear motion. Let's break this down step-by-step. ### Step 1: Understand the Problem - The car starts from rest, which means its initial velocity (u) is 0 m/s. - The acceleration (a) is given as 3 m/s². - The time (t) for which the car accelerates is 5 seconds. ### Step 2: Use the Kinematic Equation The formula to calculate the final velocity (v) when an object accelerates from rest is: \[ v = u + at \] Where: - \( v \) = final velocity - \( u \) = initial velocity - \( a \) = acceleration - \( t \) = time ### Step 3: Substitute the Values Now, we can substitute the known values into the equation: - \( u = 0 \, \text{m/s} \) - \( a = 3 \, \text{m/s}^2 \) - \( t = 5 \, \text{s} \) So, the equation becomes: \[ v = 0 + (3 \, \text{m/s}^2 \times 5 \, \text{s}) \] ### Step 4: Perform the Calculation Now, we calculate the product of acceleration and time: \[ v = 3 \, \text{m/s}^2 \times 5 \, \text{s} = 15 \, \text{m/s} \] ### Conclusion Thus, the final velocity of the car after 5 seconds is **15 m/s**. Therefore, the correct option is **C**. ### Explanation of Other Options - **Option A: 5 m/s** - This option is incorrect because it underestimates the effect of acceleration over 5 seconds. The calculation shows that the car accelerates much faster than this. - **Option B: 10 m/s** - This option is also incorrect. It suggests that the car would have reached a velocity of 10 m/s, which is not possible given the acceleration of 3 m/s² over 5 seconds. - **Option D: 20 m/s** - This option is incorrect as well. It implies that the car would have accelerated too quickly, suggesting an acceleration of 4 m/s² over 5 seconds, which is not the case. ### Common Pitfalls - **Forgetting the initial velocity**: Always remember that if an object starts from rest, its initial velocity is 0 m/s. - **Misunderstanding acceleration**: Acceleration is the rate of change of velocity. Ensure you apply it correctly over the time period given. - **Not using the correct units**: Always check that your units are consistent (e.g., m/s² for acceleration and seconds for time). ### Revision Summary - Use the kinematic equation \( v = u + at \) to find final velocity. - Substitute the initial velocity, acceleration, and time into the equation. - Perform the multiplication carefully to avoid errors. - Remember that starting from rest means the initial velocity is 0 m/s. By following these steps, you can confidently solve similar problems involving acceleration and velocity in linear motion.