A body of mass 0.4kg moving with constant speed of 10m/s to north is subjected to a constant force of 8 N directed towards the south for 30s. Take the instant the force is applied to be t=0, the position of the body at that time to be x=0 and t =-5s and t=-25s

To find the position of the body at certain times, we need to use the equations of motion. Let's break it down step by step:

Step 1: Find the acceleration of the body.
We know that force (F) equals mass (m) multiplied by acceleration (a). In this case, the force is constant at 8 N, and the mass of the body is 0.4 kg. Therefore, we can use the formula F = ma to find the acceleration:

8 N = 0.4 kg * a

Dividing both sides by 0.4 kg gives us:
a = 8 N / 0.4 kg
a = 20 m/s²

Step 2: Determine the velocity of the body.
Since the body is moving with a constant speed of 10 m/s to the north, the force acting on it must be canceling out any other forces. We know that the resultant force (F_res) is equal to mass (m) multiplied by acceleration (a) according to Newton's second law. Since there are no other forces acting on the body, we can write:

F_res = ma
0 = m * a

Substituting the mass and acceleration values, we can solve for the velocity:
0 = 0.4 kg * 20 m/s²
0 = 8 m/s

This means that the velocity of the body remains constant at 10 m/s throughout the entire 30-second period, despite the force acting on it.

Step 3: Find the position of the body.
To find the position of the body at a specific time, we can use the formula for displacement (x) as a function of initial velocity (v₀), time (t), and acceleration (a):

x = v₀t + 0.5 * at²

For the initial position at t = -5s:
x = v₀ * (-5s) + 0.5 * a * (-5 s)²

Plugging in the values, we get:
x = 10 m/s * (-5 s) + 0.5 * 20 m/s² * (-5 s)²

Simplifying:
x = -50 m - 0.5 * 20 m/s² * 25 s²
x = -50 m - 0.5 * 20 m/s² * 625 s²
x = -50 m - 0.5 * 12500 m/s²
x = -50 m - 6250 m
x = -6300 m

Therefore, at t = -5s, the position of the body is -6300 m.

For the position at t = -25s:
x = v₀ * (-25s) + 0.5 * a * (-25 s)²

Plugging in the values:
x = 10 m/s * (-25 s) + 0.5 * 20 m/s² * (-25 s)²

Simplifying:
x = -250 m - 0.5 * 20 m/s² * 625 s²
x = -250 m - 6250 m
x = -6500 m

Therefore, at t = -25s, the position of the body is -6500 m.