The speed of a car travelling on a straight road is listed below at successive intervals of 1 s :
Time (s) | 0 | 1 | 2 | 3 | 4
——- | – | – | – | – | –
Speed (m/s) | 0 | 2 | 4 | 6 | 8
Which of the following is/are correct? The car travels
- 1. with a uniform acceleration of 2 m/s².
- 2. 16 m in 4 s.
- 3. with an average speed of 4 m/s.
Select the correct answer using the code given below :
1, 2 and 3
2 and 3 only
1 and 2 only
1 only
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2017
Let’s analyze each statement based on the given speed data:
1. with a uniform acceleration of 2 m/s²: The speed increases by 2 m/s every second (0 to 2, 2 to 4, 4 to 6, 6 to 8). Acceleration = change in speed / change in time = 2 m/s / 1 s = 2 m/s². Since this value is constant, the acceleration is uniform. Statement 1 is correct.
2. 16 m in 4 s: Assuming the car starts from rest (speed = 0 at time = 0) and moves with uniform acceleration (a = 2 m/s²), the distance covered in time t is given by s = ut + (1/2)at², where u is the initial speed (0 m/s). For t = 4s, s = (0)(4) + (1/2)(2)(4)² = 0 + 1 * 16 = 16 m. Statement 2 is correct.
3. with an average speed of 4 m/s: Average speed is total distance / total time. Total distance covered is 16 m (from statement 2) and total time is 4 s. Average speed = 16 m / 4 s = 4 m/s. Statement 3 is correct.
All three statements are correct.
– Uniform acceleration means the velocity changes by the same amount in equal intervals of time.
– For uniformly accelerated motion, cinematic equations can be used to calculate distance, speed, and time.
– Average speed is calculated as total distance traveled divided by the total time taken.