• If you use a cart with half the mass, you reach _______final speed.
• If you use half the force, you reach ______ final speed.
• If you push twice as long, you cover _______ distance during pushing.
• If you use a cart with half the mass, you cover_______ distance during pushing.
If no friction, same force
half mass --> twice acceleration
v = a t so twice the speed in the same time
half
d = (1/2) a t^2
twice as long --> 4 timmes distance
a = twice with half the mass and same force
d = (1/2) a t^2
twice a ---> twice distance
• If you use a cart with half the mass, you reach a "lightened" final speed.
• If you use half the force, you reach a "slightly relaxed" final speed.
• If you push twice as long, you cover a "longer-than-usual marathon" distance during pushing.
• If you use a cart with half the mass, you cover a "light and breezy" distance during pushing.
To answer these questions, we can use the principles of Newton's second law of motion and the equations of motion.
1. If you use a cart with half the mass, you reach __half__ the final speed.
Explanation: According to Newton's second law of motion, the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. Mathematically, we can express this as F = m * a, where F is the force, m is the mass, and a is the acceleration. Rearranging the equation, we have a = F / m.
Since the force remains constant, if we decrease the mass by half, the acceleration will double (as the denominator becomes half). Assuming the acceleration occurs over the same time, the final speed will also double, resulting in reaching half the final speed compared to when using a cart with the full mass.
2. If you use half the force, you reach __half__ the final speed.
Explanation: Similarly, using Newton's second law (F = m * a), if we decrease the force by half and keep the mass constant, the acceleration will also be halved. As a result, the final speed achieved will be half of what it would have been with the full force.
3. If you push twice as long, you cover __twice__ the distance during pushing.
Explanation: This question relates to the equation of motion that connects displacement (distance covered), time, initial velocity, acceleration, and final velocity. Mathematically, it can be expressed as s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time taken.
If we push twice as long, it means the time taken (t) will double. Assuming the acceleration remains constant, the displacement (distance covered) will increase proportionately. Therefore, you will cover twice the distance compared to when you pushed for the original time.
4. If you use a cart with half the mass, you cover__the same__ distance during pushing.
Explanation: The distance covered during pushing depends on various factors such as the applied force, friction, and time taken, but mass is not directly related to the distance covered. Assuming all other factors remain constant, using a cart with half the mass will not directly affect the distance covered during pushing. Thus, the distance covered will remain the same.