Question

A train travels 400 km south in 4 hours. It then rests at the station for 2 hours. It continues its trip, traveling 600 km south in 3 hours. What is its average velocity for the entire trip?

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem (D=RT; so, R = D/T, and T = D/R).

"average speed and the average velocity on this trip" are the rate:

average aped is scalar; average velocity is a vector (includes direction)

"on this trip" means total trip distance and total trip time.

Average speed = (total linear distance) / (total time)

= (distance north + distance south) / ( (time north) + (time south) )

= (95 km + 21.9 km) / ( ( (95 km) / (70 km/hr) ) + ( (21.9 km) / (80 km/hr) ) )

= (116.9 km) / (1.63 hr)

= 71.7 km/hr

Average velocity = (final difference in position) / (total time)

= (distance north - distance south) / (total time) [note: consider north positive]

= (95 km - 21.9 km) / ( ( (95 km) / (70 km/hr) ) + ( (21.9 km) / (80 km/hr) ) )

= 44.85 km north (+44.85 km)

Note that speed and velocity should not be compared when there is a change of direction involved.Speed is just magnitude, while velocity includes direction.

The average speed in this question is determined as follows:

recall distance = rate (time)

Traveling north 95km / 70 km/h = 1.357 hours

Traveling south 21.9 km / 80 km/h = 0.274 hours

So the car traveled

(95 + 21.9) km in (1.357+0.274) hours north

116.9 km / 1.631 hr = 71.67 km/h south

Now with velocity we have to consider direction

The distance becomes

(95-21.9) since the car turns around and travels south shortening the distance from the starting point

The time remains the same

73.1 km / 1.631 hr = 44.82 km/h

Answer 2

The average velocity for the entire trip is 142.85 m/s

Step-by-step explanation:

It is given that,

Distance covered by the train, d₁ = 400 km

Time taken, t₁ = 4 hours

Distance covered by the train, d₂ = 600 km

Time taken, t₂ = 3 hours

The average velocity for the entire trip is given by total distance covered divided by total time taken. Mathematically, it is given by :

`v=(d)/(t)`

`v=(d_1+d_2)/(t_1+t_2)`

`v=(400+600)/(4+3)`

v = 142.85 m/s

So, the average velocity for the entire trip is 142.85 m/s. Hence, this is the required solution.