14.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.
Q14. Velocity-Time Graph Solution
A car continues to move with a constant velocity of 6 m s-1 for 2 minutes and then accelerates with a constant acceleration of 1 m s-2 for 6 seconds. Find the displacement of the car in the state highway.
Given:
- Initial velocity, u = 6 m s-1
- Time at constant velocity = 2 min = 120 s
- Acceleration, a = 1 m s-2
- Accelerated time = 6 s
Step 1: Displacement during constant velocity
Using formula:
s = vt
s1 = 6 × 120
s1 = 720 m
Step 2: Displacement during acceleration
Using formula:
s = ut + ½at²
s2 = 6 × 6 + ½ × 1 × (6)²
= 36 + 18
s2 = 54 m
Step 3: Total displacement
Total displacement = s1 + s2
= 720 + 54
= 774 m
Final Answer = 774 m
Velocity-Time Graph
The graph shows:
- Constant velocity of 6 m s-1 from 0 to 120 s
- Velocity increasing uniformly from 6 m s-1 to 12 m s-1 between 120 s and 126 s
