Question

A body of mass 10 kg is moving with a constant velocity of $10~m/s.$ When a constant force acts for 4 s on it, it moves with a velocity $2~m/s$ in the opposite direction. The acceleration produced in it is

• A. $3~m/s^{2}$
• B. $-3~m/s^{2}$
• C. $0.3~m/s^{2}$
• D. $0.03~m/s^{2}$

Hint:

A body of mass 10 kg is moving with a constant velocity of $10~m/s.$ When a constant force acts for 4 s on it, it moves with a velocity $2~m/s$ in the opposite direction. The acceleration produced in it is

Answer 1

The Correct Option is B

To find the acceleration produced in the body, we need to use the equation of motion that relates initial velocity, final velocity, acceleration, and time. The equation is:

\(v = u + at\)

Where:

• \(v\) = final velocity
• \(u\) = initial velocity
• \(a\) = acceleration
• \(t\) = time

In this case, the body changes its direction, which means that the final velocity is in the opposite direction to the initial velocity.

Given:

• Initial velocity, \(u = 10 \, \text{m/s}\)
• Final velocity, \(v = -2 \, \text{m/s}\) (opposite direction)
• Time, \(t = 4 \, \text{s}\)

Let's plug these values into the equation:

\(-2 = 10 + a \times 4\)

Solving for \(a\):

\(-2 = 10 + 4a\)

\(4a = -2 - 10\)

\(4a = -12\)

\(a = \frac{-12}{4} = -3 \, \text{m/s}^2\)

The acceleration produced in the body is \(-3 \, \text{m/s}^2\).

This negative acceleration indicates a deceleration, as the body changes direction and slows down. Hence, the correct option is \(-3 \, \text{m/s}^2\).