The velocity of a particle moving with a uniform acceleration of ${\text{10 ms}}^{-\text{2}}$after 5 s is ${\text{50 ms}}^{-\text{1}}$. Its velocity of the particle in the beginning of $5^{\text{th}}$ second is

velocity of 5^th second

velocity of particle at the beginning of 5^th second                             

= velocity of particle at the end of 4 sec = 40 m/s

Explanation: 

To find the velocity of the particle at the beginning of the 5th second, we use the formula:

v_n = u + a(n - 1)

Where:

• v_n: Velocity at the beginning of the n-th second
• u: Initial velocity
• a: Acceleration
• n: The second of interest

Given:

• Acceleration (a): 10 m/s²
• Time (n): 5 seconds
• Velocity after 5 seconds (v): 50 m/s

Step 1: Calculate Initial Velocity (u)

Using the equation of motion:

v = u + at

Substitute the values:

50 = u + 10 × 5

u = 50 - 50 = 0 m/s

Step 2: Calculate Velocity at the Beginning of the 5th Second

Using the formula:

v₅ = u + a(n - 1)

Substitute the values:

v₅ = 0 + 10 × (5 - 1)

v₅ = 10 × 4 = 40 m/s