On entering a state highway, a car continues to move with a constant velocity. Class 9

On entering a state highway, a car continues to move with a constant velocity. Class 9

Question 1.

On entering a state highway, a car continues to move with a constant velocity of 6 m s^-1 for 2 minutes and then accelerates with a constant acceleration 1 m s^-2 for 6 seconds. Find the displacement of the car on the state highway in the 2 min 6 s time interval by drawing a velocity-time graph for its motion. Class 9

Answer:

Given:

1. Phase 1: constant velocity = 6 m s^-1 for 2 min = 120 s
2. Phase 2: acceleration = 1 m s^-2 for 6 s (starting from 6 m s^-1)

Velocity-time graph :

Final velocity at end of Phase 2:

Using v = u + at:

v = 6 + 1 × 6

= 12 ms^-1

Displacement calculation (Area under graph):

Phase 1 displacement (rectangle):

s₁ = V × t

= 6 × 120= 720 m

Phase 2 displacement (trapezium):

s₂ = 1/2 × (u + v) × t

= 1/2 × (6 + 12) × 6

= 1/2 × 18 × 6

= 54 m

(Or using s = ut + 1/2at²: s₂ = 6 × 6 + 1/2 × 1 × 36 = 36 + 18 = 54 m)

Total displacement = s₁ + s₂ = 720 + 54 = 774 m