Question

directions: calculate the given problems. show your complete solutions. (15 points)

1. the distance the car traveled in meters at 1 sec, 2 sec, 3 sec and 4 sec were recorded in the data table below. calculate the average velocity for the car after 4 seconds.

time (sec)	distance (m)
2 sec	1 m
3 sec	1.5 m
4 sec	2 m

solution

Explanation:

Step1: Recall the formula for average velocity

The formula for average velocity \( v_{avg} \) is given by the total displacement (\( \Delta d \)) divided by the total time (\( \Delta t \)). Mathematically, \( v_{avg}=\frac{\Delta d}{\Delta t} \). Here, the initial position (at \( t = 0 \) sec) is not given, but we can consider the displacement from \( t = 0 \) to \( t = 4 \) sec. However, looking at the data, at \( t = 1 \) sec, distance is \( 0.5 \) m, \( t = 2 \) sec, \( 1 \) m, \( t = 3 \) sec, \( 1.5 \) m, \( t = 4 \) sec, \( 2 \) m. Assuming that at \( t = 0 \) sec, the distance is \( 0 \) m (since the car starts from rest or initial position is \( 0 \)), the total displacement \( \Delta d \) after \( 4 \) sec is \( 2 - 0=2 \) m, and total time \( \Delta t = 4 - 0 = 4 \) sec. Alternatively, we can also think of average velocity as the total distance traveled divided by total time (since it's moving in a straight line, displacement equals distance here).

Step2: Calculate average velocity

Using the formula \( v_{avg}=\frac{\text{Total Distance}}{\text{Total Time}} \). The total distance traveled after \( 4 \) seconds is \( 2 \) m (from the table, at \( t = 4 \) sec, distance is \( 2 \) m) and total time is \( 4 \) sec. So, \( v_{avg}=\frac{2\ \text{m}}{4\ \text{sec}} \).

Step3: Simplify the expression

\( \frac{2}{4}=0.5 \) m/s.

Answer:

The average velocity of the car after 4 seconds is \( 0.5 \) m/s.