the displacement of an object of 1 kg mass as a function of time t in x-y plane is given by x = 20t + 30t^2 and y = 25 - 40t in the units of meters
-the units of x and y are in meters and t is in seconds
-the force acting on the object is
-and then there's 5 answers
There is acceleration in the x direction only, and it equals d^x/dt^2 = 60 m/s^2
Multiply that by the mass in kg to get the force in Newtons.
To find the force acting on the object, we need to differentiate the given equations for displacement with respect to time. The force is given by Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Since acceleration is the second derivative of displacement with respect to time, we need to take the second derivatives of the given equations.
Given:
x = 20t + 30t^2
y = 25 - 40t
First, let's find the first derivatives with respect to time (t) for both x and y:
dx/dt = 20 + 60t
dy/dt = -40
Now, let's find the second derivatives by differentiating the first derivatives with respect to time:
d^2x/dt^2 = 60
d^2y/dt^2 = 0
Since the mass (m) of the object is given as 1 kg, the force acting on the object can be calculated using Newton's second law as:
F = m * a
F = 1 * (d^2x/dt^2 * i + d^2y/dt^2 * j)
F = 1 * (60 * i + 0 * j)
F = 60i
Therefore, the force acting on the object is 60 Newtons in the x-direction (assuming i represents the unit vector in the x-direction).
Note: The answer may vary depending on the unit vectors used in the given context.