Question

The graph below describes the journey of a train between two cities

Answer 1

200km/h^2, 125km, 62.5km/h

Explanation:

For part a) just use the acceleration formula (change in velocity/time). For part b), remember that distance traveled is the area under the graph. This is because displacement is the integral of velocity, meaning that you integrate to find the area (i.e. displacement). Lastly, for part c), just apply speed = distance/time because in this case, acceleration is constant.

Answer 2

Explanation:

To find : Acceleration in first 15 min . Distance between two cities Average speed of journey

Solution:

Each horizontal block is 1/8 hr = 7.5 min

Each vertical block is 10 km/hr

Time Velocity km/hr

0 Min ( 0 hr) 0

15 Min (1/4 hr) 50

45 Min (3/4 hr) 50

60 MIn ( 1 hr) 100

90 Min ( 3/2 hr) 100

120 Min ( 2hr) 0

Acceleration in first 15 min (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)

= 200 km/h²

Distance between two cities

= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

= 25/4 + 25 + 75/4 + 50 + 25

= 125

Distance between two cities = 125 km

Average Speed of journey = 125/2 = 62.5 km/hr

Acceleration in first 15 min = 200 km/h²

Distance between two cities = 125 km

Average Speed of journey = 62.5 km/hr

Hope this helps..