A 15 kg cart is pushed on a frictionless surface from rest horizontally by a 30 N force. What is the cart's acceleration?
b. How far wil it travel in 10 seconds?
c. What is its velocity at the end of 10 seconds?
(a) F = ma
(b) s = 1/2 at^2
(c) v = at
Better review the basic equations of motion.
To find the cart's acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
a.
Given:
Mass of cart (m) = 15 kg
Force applied (F) = 30 N
Acceleration (a) = F / m
Substituting the values:
Acceleration (a) = 30 N / 15 kg = 2 m/s²
Therefore, the cart's acceleration is 2 m/s².
b.
To find how far the cart will travel in 10 seconds, we can use the kinematic equation:
Distance (d) = Initial velocity (u) * Time (t) + 0.5 * Acceleration (a) * Time (t)²
Given:
Initial velocity (u) = 0 (as the cart starts from rest)
Time (t) = 10 seconds
Acceleration (a) = 2 m/s²
Substituting the values:
Distance (d) = 0 * 10 + 0.5 * 2 * (10)² = 0 + 0.5 * 2 * 100 = 0 + 1 * 100 = 100 meters
Therefore, the cart will travel 100 meters in 10 seconds.
c.
To find its velocity at the end of 10 seconds, we can use another kinematic equation:
Final velocity (v) = Initial velocity (u) + Acceleration (a) * Time (t)
Given:
Initial velocity (u) = 0 (as the cart starts from rest)
Time (t) = 10 seconds
Acceleration (a) = 2 m/s²
Substituting the values:
Final velocity (v) = 0 + 2 * 10 = 0 + 20 = 20 m/s
Therefore, the cart's velocity at the end of 10 seconds is 20 m/s.
To find the cart's acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
a. To find the cart's acceleration:
The net force can be calculated by subtracting the force of friction from the applied force. In this case, since the surface is frictionless, the force of friction is zero.
Therefore, the net force acting on the cart is equal to the applied force:
Net force = Applied force = 30 N
Using Newton's second law:
Acceleration = Net force / Mass
Acceleration = 30 N / 15 kg
Acceleration = 2 m/s^2
b. To find how far the cart will travel in 10 seconds:
We can use the kinematic equation:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Since the cart starts from rest, its initial velocity is 0 m/s.
Substituting the values:
Distance = 0 * 10 + (1/2) * 2 * (10)^2
Distance = 0 + 1 * 100
Distance = 100 meters
c. To find the cart's velocity at the end of 10 seconds:
We can use the kinematic equation:
Final velocity = Initial velocity + Acceleration * Time
Since the initial velocity of the cart is 0 m/s and the acceleration is 2 m/s^2, substituting the values:
Final velocity = 0 + 2 * 10
Final velocity = 20 m/s