NEGATIVE DIRECTION 10 MILES FOR 3 HOURS, THEN POSITIVE DIRECTION 5 MILES OVER FOR 2 HOURS. WHAT IS HIS DISPLACEMENT? SPEED? VELOCITY?
To calculate the displacement, speed, and velocity, we first need to understand the definitions of these terms:
- Displacement: It measures the change in position or the straight-line distance between the initial and final positions, regardless of the path taken.
- Speed: It measures how fast an object is moving and is calculated by dividing the total distance traveled by the time taken.
- Velocity: It specifies the speed of an object in a given direction. It is calculated by dividing the displacement by the time taken.
In this scenario, the person initially moves in the negative direction for 10 miles for 3 hours. This means their displacement in the negative direction is -10 miles.
Then, they move in the positive direction for 5 miles for 2 hours. The displacement in the positive direction is +5 miles.
To calculate the total displacement, we add up the individual displacements:
Total Displacement = Displacement in Negative Direction + Displacement in Positive Direction
= -10 miles + 5 miles
= -5 miles
Now, let's proceed to calculate the speed and velocity:
Speed = Total Distance Traveled / Total Time Taken
= (Distance in Negative Direction + Distance in Positive Direction) / (Time in Negative Direction + Time in Positive Direction)
= (10 miles + 5 miles) / (3 hours + 2 hours)
= 15 miles / 5 hours
= 3 miles per hour
Velocity = Total Displacement / Total Time Taken
= -5 miles / (3 hours + 2 hours)
= -5 miles / 5 hours
= -1 mile per hour
Therefore, the person's displacement is -5 miles, their speed is 3 miles per hour, and their velocity is -1 mile per hour.