Question

Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point c in another 1 minute. What are Joseph’s a rage speeds and velocities in jogging from A to B and from A to C

Answer 1

$\sf{\underline{We\:know\:that:}}$

$\boxed{\sf{Velocity = \frac{Displacement}{Time}} }$

$\boxed{\sf{Speed = \frac{Distance}{Time}}}$

a) When he jogs from A to B on a straight road,

$\boxed{\sf{Displacement = Distance = 300 \: m}}$

$\sf{\underline{Time:}}$

$\implies$ $\sf{2 \: minutes \: 30 \: seconds}$

$\implies$ $\sf{(2 \times 60) + 30}$

$\implies$ $\sf{120 + 30}$

$\implies$ $\sf{150 \: s}$

$\sf{\underline{Velocity:}}$

$\implies$ $\sf{ \frac{300}{150}}$

$\implies$ $\boxed{\sf{2\:m/s}}$

$\sf{\underline{Speed:}}$

$\implies$ $\sf{ \frac{300}{150}}$

$\implies$ $\boxed{\sf{2\:m/s}}$

b) When he jogs from A to B and turns back to C,

$\sf{\underline{Displacement:}}$

$\implies$ $\sf{300 - 100}$

$\implies$ $\sf{200 \: m}$

$\sf{\underline{Distance:}}$

$\implies$ $\sf{300 + 100}$

$\implies$ $\sf{400 \: m}$

$\sf{\underline{Time:}}$

$\implies$ $\sf{3 \: minutes \: 30 \: seconds}$

$\implies$ $\sf{(3 \times 60) + 30}$

$\implies$ $\sf{180 + 30}$

$\implies$ $\sf{210 \: s}$

$\sf{\underline{Velocity:}}$

$\implies$ $\sf{\frac{200}{210}}$

$\implies$ $\sf{\frac{20}{21}}$

$\implies$ $\boxed{\sf{0.952 \: m/s}}$

$\sf{\underline{Speed:}}$

$\implies$ $\sf{ \frac{400}{210}}$

$\implies$ $\sf{ \frac{40}{21}}$

$\implies$ $\boxed{\sf{1.9047 \: m/s}}$

Answer 2

Q(1)

Rage of speed and velocity in jogging from A to B

Distance (s) =300 mtrs

Displacement =300 metres

Time = 2min and 30 sec

1 min =60sec

2 min=2 x 60=120

So, time =120+30

t=150

Speed= Distance covered by an object /time taken

Speed =s/t

Speed =300/150

Speed =2m/sec

Velocity = Displacement/time taken

Velocity =300/150

Velocity =2 m/sec

Q2 rage of speed and velocity in jogging from A to C

Total distance covered=300+100=400 mtrs

Displacement = 200 metres.(AB-BC=AC, 300-100=AC, AC=200 mtrs)

Time(t) = 2min and 30 sec +1 min

=150+60

=210 sec

Speed = Distance /time

=400/210

=40/21m/sec

=1.904 (approx.) m/sec

Velocity = Displacemet/time taken

=200/210

=20/21m/sec

=0.95(approx) m/sec

Displacement is the shortest distance travelled by an object