it is just a matter of integration and using initial conditions since in general dv/dt = a it implies v = integral a dt
v(t)_x = integral a_{x}(t) dt = alpha t^3/3 + c the integration constant c can be found out since we know v(t)_x at t =0 is v_{0x} so substitute this in the equation to get v(t)_x = alpha t^3 / 3 + v_{0x}
similarly v(t)_y = integral a_{y}(t) dt = integral beta - gamma t dt = beta t - gamma t^2 / 2 + c this constant c use at t = 0 v(t)_y = v_{0y} v(t)_y = beta t - gamma t^2 / 2 + v_{0y}
so the velocity vector as a function of time vec{v}(t) in terms of components as[ alpha t^3 / 3 + v_{0x} , beta t - gamma t^2 / 2 + v_{0y} ]
similarly you should integrate to find position vector since dr/dt = v r = integral of v dt
r(t)_x = alpha t^4 / 12 + + v_{0x}t + c let us assume the initial position vector is at origin so x and y initial position vector is zero and hence c = 0 in both cases
r(t)_y = beta t^2/2 - gamma t^3/6 + v_{0y} t + c here c = 0 since it is at 0 when t = 0 we assume
r(t)_vec = [ r(t)_x , r(t)_y ] = [ alpha t^4 / 12 + + v_{0x}t , beta t^2/2 - gamma t^3/6 + v_{0y} t ]
Answer:
1 Ampere.
Explanation:
From the question given above, the following data were obtained:
Resistor 1 (R₁) = 20 ohm
Resistor (R₂) = 20 ohm
Voltage (V) = 10 V
Current (I) =?
Next, we shall determine the equivalent resistance in the circuit. This can be obtained as follow:
Resistor 1 (R₁) = 20 ohm
Resistor (R₂) = 20 ohm
Equivalent Resistance (R) =?
Since the resistors are in parallel connection, the equivalent resistance can be obtained as follow:
R = (R₁ × R₂) / (R₁ + R₂)
R = (20 × 20) / (20 + 20)
R = 400 / 40
R = 10 ohm
Finally, we shall determine the total current in the circuit. This can be obtained as illustrated below:
Voltage (V) = 10 V
Equivalent Resistance (R) = 10 ohm
Current (I) =?
V = IR
10 = I × 10
Divide both side by 10
I = 10 / 10
I = 1 Ampere
Therefore, the total current in the circuit is 1 Ampere.
Answer: (b)0.000012/k
Explanation:
The linear expansion of the metal rod is given by
where
is the linear expansion
is the initial length of the rod
is the linear expansivity
is the increase in temperature
By re-arranging the equation, we find the linear expansivity:
Answer:Density: The molecules of a liquid are packed relatively close together. Consequently, liquids are much denser than gases. The density of a liquid is typically about the same as the density of the solid state of the substance. ... Compression would force the atoms on adjacent molecules to occupy the same region of space.
Explanation:
Answer:
+5m/s
Explanation:
When doing the math we figure out that e is going to be slowing down at -4m/s² for 5 seconds. In total he is slowing down -20m/s which we take from the total speed of +25m/s to get his current new speed.
