Question

A particle moving along a straight line with a uniform acceleration covers a distance of 72 cm at the 12th second, and a distance of 120 cm at the 20th second. If the acceleration of the particle is 6 cm/s², the initial velocity (crn/sec) of the particle is most nearly:

A. 1
B. 2
C. 2.5
D. 3

Answer 1

Using the equation of motion s = ut + 1/2at², two distances covered at different times, and given acceleration, we can solve for the initial velocity, which turns out to be approximately 2 cm/s.

Step-by-step explanation:

The question involves finding the initial velocity of a particle moving with uniform acceleration. Given the distances covered at the 12th and 20th seconds and the acceleration, we can infer the particle's motion characteristics.

To provide a solution, we need to use the formula for distance covered under uniform acceleration, which is s = ut + 1/2at², where s is the distance covered, u is the initial velocity, a is the acceleration, and t is the time.

For the distances given:

• At 12th second, s = 72 cm, a = 6 cm/s², t = 12 s
• At 20th second, s = 120 cm, a = 6 cm/s², t = 20 s

Applying the formula to both cases gives us two equations, which we can solve simultaneously to find the value of u.

The correct initial velocity (option B) is most nearly 2 cm/s.