Math

Question1. Find speed and velocity for walking 400 m400 \mathrm{~m} east and 600 m600 \mathrm{~m} west in 300 s300 \mathrm{~s}.
2. Find speed and velocity for walking 400 m400 \mathrm{~m} east and 100 m100 \mathrm{~m} west in 300 s300 \mathrm{~s}.

Studdy Solution

STEP 1

Assumptions1. The person walks first400 m east, then600 m west (for the first problem) or100 m west (for the second problem). . The total time for both movements is300 s.
3. The direction east is taken as positive and west as negative.
4. Speed is the total distance covered divided by the total time taken.
5. Velocity is the total displacement (final position - initial position) divided by the total time taken.

STEP 2

First, we need to calculate the total distance covered. This is the sum of the absolute values of the distances covered in each direction.
For the first problemDistance=400m+600mDistance = |400\, m| + |-600\, m|For the second problemDistance=400m+100mDistance = |400\, m| + |-100\, m|

STEP 3

Calculate the total distance covered for each problem.
For the first problemDistance=400m+600m=1000mDistance =400\, m +600\, m =1000\, mFor the second problemDistance=400m+100m=500mDistance =400\, m +100\, m =500\, m

STEP 4

Now, we need to calculate the displacement. This is the final position minus the initial position.
For the first problemDisplacement=400m600mDisplacement =400\, m -600\, mFor the second problemDisplacement=400m100mDisplacement =400\, m -100\, m

STEP 5

Calculate the displacement for each problem.
For the first problemDisplacement=400m600m=200mDisplacement =400\, m -600\, m = -200\, mFor the second problemDisplacement=400m100m=300mDisplacement =400\, m -100\, m =300\, m

STEP 6

Now, we can calculate the speed. This is the total distance covered divided by the total time taken.
For both problemsSpeed=Distance/TimeSpeed = Distance / Time

STEP 7

Plug in the values for the distance and time to calculate the speed for each problem.
For the first problemSpeed=1000m/300sSpeed =1000\, m /300\, sFor the second problemSpeed=500m/300sSpeed =500\, m /300\, s

STEP 8

Calculate the speed for each problem.
For the first problemSpeed=1000m/300s=3.33m/sSpeed =1000\, m /300\, s =3.33\, m/sFor the second problemSpeed=500m/300s=1.67m/sSpeed =500\, m /300\, s =1.67\, m/s

STEP 9

Now, we can calculate the velocity. This is the displacement divided by the total time taken.
For both problemsVelocity=Displacement/TimeVelocity = Displacement / Time

STEP 10

Plug in the values for the displacement and time to calculate the velocity for each problem.
For the first problemVelocity=200m/300sVelocity = -200\, m /300\, sFor the second problemVelocity=300m/300sVelocity =300\, m /300\, s

STEP 11

Calculate the velocity for each problem.
For the first problemVelocity=200m/300s=0.67m/sVelocity = -200\, m /300\, s = -0.67\, m/sFor the second problemVelocity=300m/300s=m/sVelocity =300\, m /300\, s =\, m/sThe speed and velocity for the first problem are 3.33m/s3.33\, m/s and 0.67m/s-0.67\, m/s respectively. The speed and velocity for the second problem are .67m/s.67\, m/s and m/s\, m/s respectively.

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