Question

A 5% grade with a length of 3,000 ft is meeting a 2% grade with a length of 4,000 ft. If a truck starts at the beginning of the first grade at a speed of 50 mph, determine the following:

1. Speed at the end of the first grade
2. Speed at the end of the second grade

Answer 1

The slope is positive so , the road is uphill , the decrease in speed on the 5% grade road of length 3000 ft is

= Distance × Slope × Speed

= 3000 ft ×( 5/100) × 50 mph

= 0.57 × 0.05 × 50 = 1.425 mph

So,

• Speed at the end of first grade is 50-1.425 = 48.575 mph

For the second part, where the length of the road is 4000ft and the slope is 2%

The decrease in speed = Distance × Slope ×Speed

= 4000ft ×( 2/100) × 48.575

=0.76 × 0.02 × 48.575 = 0.74mph

So,

• Speed at the end of second grade

=48.575 - 0.74 = 47.835mph