Answer:
a) 
b) 
c) 
d) Displacement = 22 m
e) Average speed = 11 m/s
Explanation:
a)
Notice that the acceleration is the derivative of the velocity function, which in this case, being a straight line is constant everywhere, and which can be calculated as:
Therefore, acceleration is
b) the functional expression for this line of slope 4 that passes through a y-intercept at (0, 3) is given by:
c) Since we know the general formula for the velocity, now we can estimate it at any value for 't", for example for the requested t = 1 second:
d) The displacement between times t = 1 sec, and t = 3 seconds is given by the area under the velocity curve between these two time values. Since we have a simple trapezoid, we can calculate it directly using geometry and evaluating V(3) (we already know V(1)):
Displacement = 
e) Recall that the average of a function between two values is the integral (area under the curve) divided by the length of the interval:
Average velocity = 
Answer: 40.2 hp
Explanation:
The mass of the car is 2000kg.
in 21 seconds, it accelerates from 0m/s to 25m/s, so the average acceleration is:
a = (25m/s)/(21s) = 1.2 m/s^2
We know that force = mass*acceleration, then:
F = 2000kg*1.2m/s^2 = 2400N.
Now, the Power can be written as:
P = W/t where W is work = F*d (force per distance) and t is time.
then we have:
P = (F*d)/t and d/t is the average velocity, and we know the velocity v = 25m/s, so the average velocity will be (1/2)*25m/s = 12.5m/s
P = F*12.5m/s
and the force is F = 2400N
P = 2400 N*12.5m/s = 30,000 W
and we know that 1hp = 746 W
then, P = (30,000/746) hp = 40.2 hp
2H2O->2H2+O2
This balanced chemical equation represents the decomposition of water into hydrogen gas and oxygen gas
Answer:
Graph for object that is not moving: B
Graph for object that is speeding up: D
Explanation:
A.) In order to represent that an object is not moving, you must either show that there is no velocity (0 m/s) or show a position over time graph that is a horizontal line.
Because the position is the same as time increases, the graph shows that there the object must be at rest, as there is no change in position due to velocity. (Velocity must be 0m/s)
B.) In order to represent an object is speeding up, the position time graph must either be a positive exponential function, the velocity time graph must be a positive, linear line, or the acceleration over time graph must be a positive, horizontal line.
Why is D the correct answer? Because if an object is speeding up, you know that the value of its speed (velocity) is increasing at some rate. And since speeding up refers to positive change, the function of velocity over time graph must be a positive function.
Answer:
1.603 s
Explanation:
Given that
Initial mass, = 0.45 kg
Initial period, = 1.45 s
Initial radius, = 0.14 m
Final mass, = 0.55 kg
Final period, = ?
Final radios, = 0.14 m
Since we are finding the rotation period of two masses of same radius, we can assume that the outward force is the same in both cases. This means that
m₁r₁ω₁² = m₂r₂ω2²
Where, ω = 2π/T, on substituting, we have
0.45 * 0.14 * (2π / 1.45)² = 0.550 * 0.14 * (2π / T₂)²
0.45 / 1.45² = 0.550 / T₂²
T₂² = 0.550 * 1.45² / 0.45
T₂² = 2.56972
T₂ = √2.56972
T₂ = 1.603 sec
