Question

A body of mass 5 kg is initially at rest on a smooth horizontal surface. A constant force of 20 N is applied to the body. Find the acceleration of the body and the distance traveled by the body in 10 seconds.

• A. \( 2 \, \text{m/s}^2 \), \( 50 \, \text{m} \)
• B. \( 4 \, \text{m/s}^2 \), \( 80 \, \text{m} \)
• C. \( 4 \, \text{m/s}^2 \), \( 40 \, \text{m} \)
• D. \( 2 \, \text{m/s}^2 \), \( 100 \, \text{m} \)

Hint:

When a body is acted upon by a constant force on a smooth surface, the acceleration will be constant and can be calculated using \( F = ma \). The distance traveled can then be found using the equations of motion.

Answer 1

The Correct Option is A

We are given the following information: - Mass of the body, \( m = 5 \, \text{kg} \), - Applied force, \( F = 20 \, \text{N} \), - Initial velocity of the body, \( u = 0 \, \text{m/s} \) (since the body is initially at rest), - Time duration, \( t = 10 \, \text{s} \). The first part of the question asks to find the acceleration of the body. According to Newton's Second Law of Motion: \[ F = ma \] Where: - \( F \) is the applied force, - \( m \) is the mass, - \( a \) is the acceleration. Rearranging the equation to solve for \( a \): \[ a = \frac{F}{m} \] Substituting the given values: \[ a = \frac{20}{5} = 4 \, \text{m/s}^2 \] So, the acceleration of the body is \( 4 \, \text{m/s}^2 \). The second part of the question asks to find the distance traveled by the body in 10 seconds. We can use the equation for motion under constant acceleration: \[ s = ut + \frac{1}{2}at^2 \] Where: - \( s \) is the distance traveled, - \( u \) is the initial velocity, - \( a \) is the acceleration, - \( t \) is the time. Substituting the known values: \[ s = 0 \times 10 + \frac{1}{2} \times 4 \times 10^2 \] \[ s = \frac{1}{2} \times 4 \times 100 = 200 \, \text{m} \] Thus, the distance traveled by the body in 10 seconds is \( 200 \, \text{m} \).