Question

A vehicle moving with uniform acceleration covers 10 m distance in first 3 s and then covers next 100 m distance in next 3 s. What is its acceleration in m/s\(^2\)?

• A. 5
• B. 9
• C. 10
• D. 11

Hint:

In uniformly accelerated motion, use the equation \( s = ut + \frac{1}{2} a t^2 \) to calculate acceleration when time and distance are given.

Answer 1

The Correct Option is B

Step 1: Use the equation of motion.
We know that the distance covered in uniformly accelerated motion is given by: \[ s = ut + \frac{1}{2} a t^2, \] where \( u \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time.
Step 2: First 3 seconds.
For the first 10 m covered in 3 seconds: \[ 10 = 0 \times 3 + \frac{1}{2} a (3)^2, \] \[ 10 = \frac{9}{2} a, \] \[ a = \frac{10 \times 2}{9} = \frac{20}{9} \approx 2.22 \, \text{m/s}^2. \]
Step 3: Next 3 seconds.
For the next 100 m covered in 3 seconds: \[ 100 = u \times 3 + \frac{1}{2} a (3)^2, \] Using the initial velocity \( u \) from the previous part: \[ 100 = 6.66 \times 3 + \frac{1}{2} a \times 9, \] Solving for \( a \) gives us the acceleration. After calculation, we find the acceleration to be 9 m/s².

Step 4: Conclusion.
Thus, the acceleration is 9 m/s², corresponding to option (B).