Final answer:
To reach a velocity of 20 m/s, a 4kg brick needs to have a force of 160N applied to it for 0.5 seconds.
Step-by-step explanation:
To find the time for which a force is applied to reach a certain velocity, we can use Newton's second law of motion, which states that F = ma, where F is the force applied, m is the mass of the object, and a is the acceleration produced. In this case, the force applied is 160N and the mass of the brick is 4kg. We need to calculate the acceleration produced. Since velocity is the rate of change of displacement, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken. Rearranging this equation, we have t = (v - u) / a. Plugging in the values, we get t = (20 - 0) / a. Rearranging again, we can find the acceleration produced, a = (v - u) / t. Plugging in the values, we get a = (20 - 0) / t. Now we can solve for t, t = 20 / a. Plugging in the value of a, t = 20 / (160 / 4). Simplifying, t = 20 / 40 = 0.5 seconds. So, the force of 160N needs to be applied for 0.5 seconds to reach a velocity of 20 m/s.