Question

If a body moving with uniform acceleration travels a distance of 10 m in the first 10 s, then how much total distance in m will it cover at the end of 30 s from the beginning?

• A. 30
• B. 50
• C. 70
• D. 90

Hint:

Use the equation \( s = \frac{1}{2} a t^2 \) to calculate the distance covered in uniformly accelerated motion.

Answer 1

The Correct Option is D

Step 1: Use the equation of motion.
The equation for the distance traveled under uniform acceleration is: \[ s = ut + \frac{1}{2} a t^2. \] Since the body starts from rest, \( u = 0 \), so the equation becomes: \[ s = \frac{1}{2} a t^2. \]
Step 2: Find the acceleration.
For the first 10 m in 10 seconds, we use: \[ 10 = \frac{1}{2} a (10)^2, \] \[ 10 = 50a \quad \Rightarrow \quad a = \frac{10}{50} = 0.2 \, \text{m/s}^2. \]
Step 3: Calculate the distance after 30 seconds.
Now, using \( a = 0.2 \, \text{m/s}^2 \), calculate the distance traveled in 30 seconds: \[ s = \frac{1}{2} \times 0.2 \times (30)^2 = \frac{1}{2} \times 0.2 \times 900 = 90 \, \text{m}. \]
Step 4: Conclusion.
Thus, the total distance traveled after 30 seconds is 90 meters, which corresponds to option (D).

Answer 2

This question asks for the total distance covered in 30 s by a body starting from rest with uniform acceleration, given it covers 10 m in the first 10 s. Instead of directly solving for the acceleration, we can split the 30 s into three equal 10 s intervals and use the fact that for uniform acceleration from rest, the distances covered in successive equal time intervals are in the ratio of consecutive odd numbers: \( 1:3:5 \). Since the first interval covers 10 m, this 10 m represents "1 unit" of the ratio, so the second interval covers 3 units (30 m) and the third covers 5 units (50 m). Let's check each option against the running total.

1. 30: This does not correspond to the cumulative distance at any of the three interval boundaries here (the cumulative total after two intervals is 40 m, not 30 m), so it is incorrect.
2. 50: This equals the distance covered in the third interval ALONE (5 units × 10 m = 50 m), not the total distance from the beginning through 30 s, so it is incomplete and incorrect as a final answer.
3. 70: This does not correspond to any correct partial or full sum of the interval ratios here, so it is incorrect.
4. 90: Adding all three intervals, the total ratio is \( 1+3+5 = 9 \) units, giving \( 9 \times 10 = 90 \) m, which is exactly the cumulative distance covered from the start through 30 s.

Using the odd-number ratio rule for uniformly accelerated motion from rest confirms the total distance after 30 s is 90 m.

Therefore, the correct answer is 90 m.