1st derivative gives velocity;
d r(t)/ dt = 2t i + 6 j + 4/t k
2nd derivative gives acceleration;
d^2 r(t)/ dt^2 = 2 i - 4/ t^2
Speed ;
Square root of (4 t^2 + 36 + 16/ t^2)
For a given time, like 2 seconds, t will be 2. And answer of speed will be scalar.
Answer:
B. An Iron Bar place in a room becomes cooler than its surroundings.
Answer:
b, a, c
Explanation:
The middle one has the shortest wavelength, then it's the top one and the last one has the longest wavelength.
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:
"Why"
Explanation: A scientific law is a description of how the natural world behaves under certain circumstances.