Question

A vehicle starts off from rest and reaches a velocity of 80 km/h in 12 seconds. If the velocity increases uniformly, how far will the train travel in the first 12 seconds? Verify your calculations by drawing a velocity versus time graph. Answer to 2 decimal places

Answer 1

First convert the speed to m/s:
80 km/h = 80 × (1000 m / 3600 s) = 200/9 m/s ≈ 22.222... m/s.

With uniform acceleration from rest, distance in time t is
s = (average velocity) × t = ((0 + v)/2) × t = (v/2) t.

For v = 200/9 m/s and t = 12 s:
s = (200/9 ÷ 2) × 12 = (200/9) × 6 = 1200/9 = 400/3 ≈ 133.333... m.

To two decimal places: 133.33 m.

Verification by v–t graph:
Plot v(t) as a straight line from (0 s, 0 m/s) to (12 s, 200/9 m/s). The distance traveled is the area under this line, a triangle of base 12 s and height 200/9 m/s, so
area = 1/2 × 12 × (200/9) = 400/3 ≈ 133.33 m,
matching the calculation above.