To determine the mass of the cart, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given: Force (F) = 80 N Acceleration (a) = 3 m/s²
Using the formula F = m * a, where F is the force, m is the mass, and a is the acceleration, we can rearrange the formula to solve for mass:
m = F / a
Plugging in the values, we get:
m = 80 N / 3 m/s² = 26.67 kg (rounded to two decimal places)
So, the mass of the cart is approximately 26.67 kg.
To find the velocity of the cart after 4.0 seconds, we can use the formula for uniformly accelerated motion:
v = u + a * t
where v is the final velocity, u is the initial velocity (which is zero in this case since the cart starts from rest), a is the acceleration, and t is the time.
Given: Initial velocity (u) = 0 m/s Acceleration (a) = 3 m/s² Time (t) = 4.0 s
Plugging in the values, we have:
v = 0 m/s + 3 m/s² * 4.0 s v = 0 m/s + 12 m/s v = 12 m/s
So, the velocity of the cart after 4.0 seconds is 12 m/s.