A truck driver driving at the speed of 54 km h-1 notices a road sign with a speed limit. Class 9

A truck driver driving at the speed of 54 km h^-1 notices a road sign with a speed limit. Class 9

Question 1.

A truck driver driving at the speed of 54 km h^-1 notices a road sign with a speed limit of 40 km h^-1 for trucks. He slows down to 36 km h^-1 in 36 s. What was the distance travelled by him during this time? Assume the acceleration to be constant while slowing down. Class 9

Answer:

Given:

1. Initial velocity, u = 54 km h^-1 = 54 × (1000/3600) = 54/3.6 = 15 m s^-1
2. Final velocity, v = 36 km h^-1 = 36/3.6 = 10 m s^-1
3. Time, t = 36 s
4. Acceleration is constant Finding acceleration:

a = (v - u) /1 = (10 - 15) / 36 = -5 / 36 m s^-2

Finding distance travelled using s = ut + 1/2at²:

s = 15 × 36 + 1/2 × (-5/36) × (36)²

s = 540 + 1/2 × (-5/36) × 1296

s = 540 + (-5/36) × 648

s = 540 - 90

s = 450 m

Verification using v² = u² + 2as:

10² = 15² + 2 × (-5/36) × s

100 = 225 - (10/36) × s

(10/36) × s = 125

s = 125 × 36/ 10 = 450 m