A car accelerates uniformly from 18 km/h to 72 km/h in 5 seconds. What is the magnitude of its acceleration in m/s^2?

Introduction / Context:
Uniform acceleration problems involving speed changes are very common in basic kinematics. This question asks you to find the acceleration of a car that speeds up from a lower speed to a higher speed over a known time interval. Since the speeds are given in kilometres per hour, an important part of the solution is converting them correctly into metres per second, which is the standard unit used in most physics formulas. Understanding how to perform this conversion and then apply the acceleration formula is essential for solving motion problems in examinations and practical scenarios such as vehicle dynamics.

Given Data / Assumptions:
• Initial speed u = 18 km/h. • Final speed v = 72 km/h. • Time interval t = 5 s. • Motion is along a straight line with uniform acceleration. • Air resistance and friction are neglected for this calculation.

Concept / Approach:
Acceleration is defined as the rate of change of velocity with respect to time. For uniform acceleration, we use the simple relation a = (v - u) / t. However, the velocities in this problem are given in km/h, while time is in seconds and acceleration is asked in m/s^2. Therefore, before applying the formula, we need to convert the speeds from km/h to m/s using the standard conversion factor 1 km/h = 5 / 18 m/s. After converting both initial and final speeds into m/s, we substitute them into the acceleration formula and simplify.

Step-by-Step Solution:
Step 1: Convert the initial speed to m/s. Step 2: u = 18 km/h = 18 * (5 / 18) m/s = 5 m/s. Step 3: Convert the final speed to m/s. Step 4: v = 72 km/h = 72 * (5 / 18) m/s = 20 m/s. Step 5: Use the formula for uniform acceleration a = (v - u) / t. Step 6: Substitute v = 20 m/s, u = 5 m/s, t = 5 s to get a = (20 - 5) / 5 = 15 / 5 = 3 m/s^2.

Verification / Alternative check:
We can quickly verify the reasonableness of the answer. The speed change is from 5 m/s to 20 m/s, a difference of 15 m/s. If this change happens evenly over 5 s, then the car gains 3 m/s of speed every second. This is a moderate, realistic acceleration for a car that is speeding up on a road. The magnitude is neither extremely small nor unreasonably large, so 3 m/s^2 is a plausible and consistent value.

Why Other Options Are Wrong:
Option b (5 m/s^2): This corresponds to a much larger change in speed than actually occurs and does not match the detailed calculation. Option c (6 m/s^2): This would require a speed change of 30 m/s over 5 s, which is double the actual change. Option d (7 m/s^2): This implies an even greater acceleration and is not compatible with the given speeds and time. Option e (2 m/s^2): This would correspond to a total speed change of only 10 m/s in 5 s, which is smaller than the actual 15 m/s change.

Common Pitfalls:
A frequent mistake is forgetting to convert from km/h to m/s and directly substituting the values into formulas, which leads to wrong units for acceleration. Another error is converting only one of the speeds instead of both. Sometimes students also misapply the formula and use t in minutes or hours instead of seconds. Always ensure that speeds are in m/s, time is in seconds, and acceleration is in m/s^2. Carefully check unit conversions and subtraction order (v minus u, not u minus v) to avoid sign errors.

Final Answer:
The acceleration of the car is 3 m/s^2.