Question

An object having a velocity of 5 m/s is accelerated at the rate 2 m/s\(^2\) for 6s. Find the distance travelled during the period of acceleration.

• A. 60 m
• B. 25 m
• C. 36 m
• D. 66 m
• E. 45 m

Hint:

The formula \( S = ut + \frac{1}{2} a t^2 \) is crucial for calculating the distance travelled under uniform acceleration. Remember to substitute the correct values for initial velocity, acceleration, and time.

Answer 1

The Correct Option is D

Step 1: Understanding the equation for distance.
The equation to calculate the distance travelled under uniform acceleration is: \[ S = ut + \frac{1}{2} a t^2 \] Where:
- \( u = 5 \, \text{m/s} \) (initial velocity)
- \( a = 2 \, \text{m/s}^2 \) (acceleration)
- \( t = 6 \, \text{s} \) (time)

Step 2: Substituting values in the equation.
Substitute the values of \( u \), \( a \), and \( t \) into the formula: \[ S = 5 \times 6 + \frac{1}{2} \times 2 \times 6^2 \]

Step 3: Simplifying the equation.
Simplifying the terms: \[ S = 30 + \frac{1}{2} \times 2 \times 36 = 30 + 36 = 66 \, \text{m} \]

Final Answer: 66 m