Question

Joseph jogs from one A to the other end B of a straight 300 m road in 2
minutes 50 seconds and then turns around and jogs 100 m back to point
C in another 1 minute. What are Joseph's average speeds and velocities
in jogging(a) from A to B and (b) from A to C?​

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \: Solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Question...}}}}}$

⋆ Correct question: Joseph jogs from one A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph's average speeds and velocities in jogging (a) from A to B and (b) from A to C?

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

⋆ Joseph jogs from one A to the other end B of a straight 300 m road in 2 minutes 50 seconds.

⋆ Then he turns around and jogs 100 m back to point C in another 1 minute.

${\bigstar \:{\pmb{\sf{\underline{To \: find...}}}}}$

⋆ Average speeds

• From A to B
• From A to C

⋆ Average velocities

• From A to B
• From A to C

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ Average speeds

• From A to B = 1.76 m/s
• From A to C = 1.73 m/s

⋆ Average velocities

• From A to B = 1.76 m/s
• From A to C = 0.86 m/s

${\bigstar \:{\pmb{\sf{\underline{Using \: concepts...}}}}}$

⋆ Average speed is given by

• Total distance/Total time

⋆ Average velocity is given by

• Total displacement/Total time

⋆ 1 minute converted into seconds by

• 1 minute = 60 seconds

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

~ Firstly let us convert minutes into seconds in the both cases

Case 1st

→ 2 minutes 50 seconds

→ 2 × 60 + 50

→ 120 + 50

→ 170 seconds

Case 2nd

→ 1 minute

→ 1 × 60

→ 60 seconds

~ Now let us find out the average speed and average velocity in case 1st

Average speed 1st

→ Total distance/Total time

→ 300/170

→ Average speed = 1.76 m/s

Average velocity 2nd

→ Total displacement/Total time

• Displacement is the shortest distance, here shortest distance is 300 metres itself.

→ 300/170

→ Average velocity = 1.76 m/s

~ Now let's find out the average speed and average velocity in case 2nd

Average speed 1st

• Here, the total distance be AB + BC therefore, 300 + 100 = 400 metres.

• Here the total time be AB + BC therefore, 170 + 60 = 230 seconds

→ Total distance/Total time

→ 400/230

→ Average speed = 1.73 m/s

Average velocity 2nd

→ Total displacement/Total time

• Displacement is the shortest distance, here shortest distance is AB - BC that is 300 - 100 = 200 metres.

→ 200/230

→ Average velocity = 0.86 m/s