If a car's speed is decreasing over time, what can you conclude about its acceleration?
The acceleration is positive.
The acceleration is negative.
The acceleration is zero.
Nothing about the acceleration can be determined.
Correct Answer :
B. The acceleration is negative.
Related Questions
What is the limit of (sin x) / x as x approaches 0?
1
0
-1
Undefined
The area between the curve y = x^2 and the x-axis from x = 0 to x = 2 is equal to:
2
4
8/3
16/3
Which method is commonly used to solve separable differential equations?
Laplace transforms
Substitution
Separation of variables
Variation of parameters
If f(x) = sin(x), what is f'(x)?
cos(x)
-cos(x)
sin(x)
-sin(x)
If the velocity of an object is given by v(t) = 3t^2, what does ?(1 to 2) v(t) dt represent?
The total distance traveled by the object from t = 1 to t = 2
The acceleration of the object at t = 1
The change in velocity of the object from t = 1 to t = 2
The displacement of the object at t = 2
If f(x) = 3x^2 - 2x + 1, what is the value of f(4)?
25
33
41
49
What is the equation of a sphere with center (1, -2, 3) and radius 4?
(x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 4
(x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 16
(x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 4
(x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 16
If a point has polar coordinates (r, ?), what are its Cartesian coordinates?
x = rcos(?), y = rsin(?)
x = r?, y = r?
x = cos(?), y = sin(?)
x = rsin(?), y = rcos(?)
What is the line integral ?C F � dr, where C is a curve in the xy-plane and F = ?
It depends on the specific curve C.
It is always zero.
It is equal to the area enclosed by C.
It is equal to the circumference of C.
What is the unit vector in the direction of vector v = <4, -3>?
<1, 1>
<2, -1.5>
<4/5, -3/5>
<0, 0>
Which technique of integration is used to evaluate the integral of a product of two functions, often when integration by parts is required?
Trigonometric substitution
Integration by substitution
Integration by partial fractions
Integration by u-substitution
Which of the following is an exact differential equation?
dy/dx = 2xy
dy/dx = x^2 + y^2
dy/dx = e^x
dy/dx = y^2 - x^2
Which test is used to determine the convergence or divergence of an infinite series involving alternating terms?
Integral Test
Comparison Test
Alternating Series Test
Divergence Test
What does the definite integral ?(a to b) f(x) dx represent geometrically?
The average value of f(x) on [a, b]
The area between the curve y = f(x) and the x-axis on [a, b]
The derivative of f(x) at x = a
The slope of the tangent line to the curve y = f(x) at x = b
In three-dimensional space, what are the coordinates of the origin?
(0, 0, 0)
(1, 1, 1)
(0, 0)
(1, 1)
What is the area of the region enclosed by the polar curve r = 2sin(?)?
p square units
4 square units
2 square units
0 square units
What is the antiderivative of e^(2x) with respect to x?
e^(2x) + C
(1/2)e^(2x) + C
(1/2)e^(2x^2) + C
(1/4)e^(2x) + C
What is the equation of the polar curve r = 2cos(?)?
A circle centered at the origin
A cardioid
A parabola
A line
Which type of differential equation is represented by the equation dy/dx = k*y, where k is a constant?
Separable
Linear
Exact
Homogeneous
In parametric equations, what do the variables x and y depend on?
Time t
Angle ?
Radius r
Both a and b
If f(x) = x^3 + 2x^2 - 5x + 1, what is f''(x)?
3x^2 + 4x - 5
6x + 4
6x^2 + 4
3x^2 + 4
What is the area under the curve y = sin(x) from x = 0 to x = p?
0
1
p
2p
The integral ?(0 to 1) x^3 dx is equal to:
0
1/4
1/3
1/2
What is the integral of e^(3x) with respect to x?
(1/3)e^(3x) + C
3e^(x) + C
(1/3)e^(x) + C
e^(3x) + C
What is the average value of the function f(x) = 2x^2 on the interval [1, 3]?
4/3
8/3
16/3
32/3
What is the integral of 3x^2 with respect to x?
x^3 + C
x^2 + C
x^3/3 + C
3x + C
What is the derivative of the constant function f(x) = 7?
0
1
7
-7
What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?
y = x^2 + 1
y = x^2
y = 2x + 1
y = 2x
What is the integral of 1/(x^2 + 1) with respect to x?
arctan(x) + C
ln(x^2 + 1) + C
2arctan(x) + C
(1/2)ln(x^2 + 1) + C
The solution to the logistic differential equation dy/dx = ky(1 - y) is often used to model population growth. What happens to the population when y = 1?
The population is increasing.
The population is decreasing.
The population is zero.
The population remains constant.