Kinematics
This is the integral of velocity
What is displacement
This quantity is found by evaluating the integral of force with respect to position.
What is Work?
the impulse object a delivers on identical object b if the force of the collision is 10t-5 and the collision happens between t=2 and t=10
440 N*S
This is the reason the center of mass of a rod with density lambda(x) cannot be found using a simple average of its endpoints
What is non‑uniform density?
These quantities decreases as two masses move farther apart in Newtonian gravity
What is Gravitational Force and Graviational Acceleration(Gravitational Field Force)
The velocity of an object at time t=4, given that it starts from rest at time t=0, and its acceleration is a(t)=3t^2+2t+1
What is 84 m/s
This is how you find delta U when given F(x)
its the negative integral of F(x)dx
The net impulse from t=2 to t=5 on a rocket falling to earth with mass 1200 kg and engines delivering force f(t)=30t^2 +10t-5 if air resistance is negligible
−34020 N*S
This quantity must be integrated to find the center of mass of any object with variable density.
What is x dm?
This is the reason the gravitational force of a planet must be integrated when calculating work done over large distances.
What is the force varies with 1/(r^2)?
This is the particle's position function given a(t)=6t−4, v(0)=2 and x(2)=10
What is t^3-2t^2+2t+6
This is the difference in the initial total mechanical energy and total mechanical energy some time later if conservative force F(x)=-20x^2 +2x-17 acts on the object
what is 0
A rocket in deep space starts at rest with mass m(t)=1200-4t kg due to fuel burn. Its engines exert a thrust force F(t)=200e^(−0.1t) N. This is the impulse delivered by the engines from t=0 to t=20 in
1729.33 N*S
This is the way to find the center of mass of an object given linear density and length l. (Equation with bounds of integration in variable form)
what is integral from 0 to l of lambda times x dx over integral from 0 to l of lambda dx
This is the quantity whose negative derivative gives the gravitational force in a central field
What is gravitational potential energy
A particle moves along a straight line with velocity v(t)=t^3−6t+4. At t=0, the particle is at x=2. This is the total distance traveled by the particle over the interval t=0 to t=4
What is 18 meters?
A particle moves under a force F(x)=6x with mass 2. Starting from rest at x=0, this is the particle’s speed when it reaches x=4.
What is sqrt 48 m/s?
Object A, of mass 2kg initially moving in the positive direction collides with identical object B initially at rest on a rough surface. The collision happens between time t=0 and time t=2. From t=0 to t=8 the acceleration of object B is given as a(x)=-e^-x (x^2+2x+2). The impulse delivered by Object A on Object B if the force of friction between the block and the ground is 5N is this.
What is 2.9 N*S
A thin rod of length L has linear mass density lambda(x)=3x. Measured from the left end, this is the rod’s center‑of‑mass position.(In variable form.)
What is 3L/4
A mass m moves from radius r1 to r2 in a gravitational field. This is the work done by gravity.
What is GMm(1/(rsub2−1/(rsub1))
A particle moves with velocity v(t)=4e^−t −2. At t=0, its position is x(0)=5. This is the total distance traveled by the particle from t=0 to t=6
what is 9.24 m?
A particle moves in the potential U(x)=4x^3 and has mass 6g. Released from rest at x=1, this is the particle’s speed when it reaches x=0.
what is 2m/s
A 3 kg drone experiences a time‑dependent horizontal force Fx(t)=12t−4, and a vertical force Fy(t)=6sin(t). Air resistance is negligible. From t=1 to t=7, this is the magnitude of the net impulse vector delivered to the drone
approx 264N*s
Two particles of masses m and 2m move along a line with positions x1(t)=t2, x2(t)=4t. This is the acceleration of the center of mass. (in variable form)
What is 2/3(2t+4)?
A mass m is released from rest at distance R from a planet of mass M. Ignoring atmosphere, this is its speed when it reaches the surface at radius R/2?
What is sqrt(2GM(2/R0)-(1/(R/2))
or sqrt((2GM)/R)