An object in space is initially stationary relative to the Earth. Then, a force begins acting on the object, starting with a force of 0 N, and increasing at a uniform rate until the magnitude of the force is 56 N after the force has acted for 10 s. The body has a mass of 15 kg. What is the speed of the object at 10 s?

a=56/15 * t/10

a= dv/dt

dv= 56/150 t dt

v= INT dv= 28/150 t^2 from zero to 10

vf=2800/150 m/s

To find the speed of the object at 10 seconds, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the force acting on the object is changing with time, so we need to find the acceleration first.

Since the force is increasing at a uniform rate, we can assume that the force is changing linearly with time. This means that the force at any given time is directly proportional to the time.

We can write the equation for the force as: F = kt, where F is the force at time t, and k is the proportionality constant.

Given that the force is 0 N initially and reaches 56 N after 10 seconds, we can plug these values into the equation to solve for the proportionality constant k.

When t = 0, F = 0: 0 = k(0)
So we know that k = 0.

Now we can find the force at any given time t using the equation: F = 0t = 0 N.

The net force acting on the object can be calculated as:
net force (Fnet) = mass (m) × acceleration (a)

Since the net force is equal to the force acting on the object, we have:
Fnet = ma

Therefore, we can equate the force and the net force to find the acceleration at any given time:
0 = ma
a = 0.

This means that the object is not accelerating, and its speed remains constant at all times. Therefore, the speed of the object at 10 seconds is 0 m/s, the same as its initial speed.

Note: It's important to interpret the problem correctly, as the wording could sometimes lead to confusion. In this case, the force is increasing with time, but the body's speed does not change because the net force on it remains zero.