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).