Respuesta :
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:
The average velocity for the entire trip is 142.85 m/s
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 :
[tex]v=\dfrac{d}{t}[/tex]
[tex]v=\dfrac{d_1+d_2}{t_1+t_2}[/tex]
[tex]v=\dfrac{400+600}{4+3}[/tex]
v = 142.85 m/s
So, the average velocity for the entire trip is 142.85 m/s. Hence, this is the required solution.
