Question

A car accelerates uniformly from 20 km/h to 50 km/h in 4 seconds. What is its acceleration?

Answer 1

To calculate the acceleration of the car, we first need to convert the speeds from kilometers per hour (km/h) to meters per second (m/s).

1. Convert the initial speed (20 km/h) to m/s:
\[
20 \text{ km/h} = \frac{20 \times 1000 \text{ m}}{3600 \text{ s}} = \frac{20000}{3600} \approx 5.56 \text{ m/s}
\]

2. Convert the final speed (50 km/h) to m/s:
\[
50 \text{ km/h} = \frac{50 \times 1000 \text{ m}}{3600 \text{ s}} = \frac{50000}{3600} \approx 13.89 \text{ m/s}
\]

3. Now that we have both speeds in m/s, we can calculate the acceleration using the formula:
\[
a = \frac{\Delta v}{\Delta t}
\]
where \(\Delta v\) is the change in velocity and \(\Delta t\) is the change in time.

4. Calculate the change in velocity (\(\Delta v\)):
\[
\Delta v = v_f - v_i = 13.89 \text{ m/s} - 5.56 \text{ m/s} = 8.33 \text{ m/s}
\]

5. The time interval (\(\Delta t\)) is given as 4 seconds.

6. Now, substitute these values into the acceleration formula:
\[
a = \frac{8.33 \text{ m/s}}{4 \text{ s}} \approx 2.08 \text{ m/s}^2
\]

Therefore, the acceleration of the car is approximately **2.08 m/s²**.