Question

A body is moving along a straight line with initial velocity v₀. Its acceleration a is constant. After t seconds, its velocity becomes v. The average velociy of the body over the given time interval is

• A. $\bar{v}=\frac{v^2+{v_0}^2}{2at}$
• B. $\bar{v}=\frac{v^2+{v_0}^2}{at}$
• C. $\bar{v}=\frac{v^2-{v_0}^2}{2at}$
• D. $\bar{v}=\frac{v^2-{v_0}^2}{at}$

Answer 1

The Correct Option is C

Given: 

• Initial velocity: $v_0$
• Final velocity after $t$ seconds: $v$
• Acceleration: $a$ (constant)

Step 1: Using Kinematic Equation

We use the third equation of motion:

$$v^2 = v_0^2 + 2 a s$$

Solving for $s$ (displacement):

$$s = \frac{v^2 - v_0^2}{2a}$$

Step 2: Average Velocity Formula

Average velocity is given by:

$$\bar{v} = \frac{\text{total displacement}}{\text{total time}}$$

$$\bar{v} = \frac{s}{t} = \frac{v^2 - v_0^2}{2at}$$

Step 3: Conclusion

The correct answer is:

$$\bar{v} = \frac{v^2 - v_0^2}{2at}$$

Answer: The correct option is C.