NEW
Font size
WorksheetsMCQ Unit 1: Kinematics
Total questions: 33
Worksheet time: 41mins
A plane starts at rest on a straight runway. For the first 30 s, the plane’s acceleration α is given as a function of time t by the equation α = βτ2, where β = 1/90 m/s4 and t is in seconds. What is the plane’s speed at t = 30 s ?
10 m/s
30 m/s
100 m/s
150 m/s
300 m/s
A small particle starts from rest from the origin of an xy-coordinate system and travels in the xy-plane. Its acceleration in the x-direction is 2.0 m/s2 , and its acceleration in the y-direction is 1.0 m/s2 . What is the x-coordinate of the particle when its y-coordinate is 12 m?
3.0 m
6.0 m
12 m
24 m
48 m
An airplane travels horizontally at a constant velocity v. An object is dropped from the plane, and one second later another object is dropped from the plane. If air resistance is negligible, what happens to the vertical distance between the two objects while they are both falling?
it increases.
it decreases.
it remains the same.
it depends on the mass of the objects.
it depends on the horizontal speed of the plane.
An equation for the motion of an object is given as 2vt - 4x = Bt 2 , where B is a constant. The variable v indicates velocity, in meters per second; t indicates time, in seconds; and x indicates displacement, in meters. What is the unit of measure for B ?
s
m/s
m/s2
m2/s
m2/s2
An object falls freely from rest under the influence of gravity. If air resistance is negligible, the ratio of the distances traveled during each 1-second time interval by the object during the first, second, and third seconds of its fall is
1:1:1
1:2:3
1:2:4
1:3:5
1:4:9
At time t = 0 , a ball is thrown with initial speed v0 at an angle θ above the horizontal. Air resistance is negligible. Which of the following best represents the speed of the ball as a function of time t while the ball is in flight?
vo sin θ - gt
vo cos θ - gt
vo2cos2θ+(vosinθ−gt)2
(vocosθ−gt)2+vo2 sin2θ
(vocosθ−gt)2+(vosinθ−gt)2
A ball of mass 2.0 kg is thrown vertically upward from the top of a building. The ball’s velocity v is given as a function of time t by the equation v(t) = R - St, where R = 5 m/s and S = 10 m/s2. The positive direction is upward.
At what time does the ball reach its maximum height above the building?
0.2 s
0.4 s
0.5 s
1.0 s
2.0 s
A ball of mass 2.0 kg is thrown vertically upward from the top of a building. The ball’s velocity v is given as a function of time t by the equation v(t) = R - St, where R = 5 m/s and S = 10 m/s2. The positive direction is upward.
If the ball reaches the ground at t = 2.0 s, what is the height of the building?
5 m
10 m
15 m
20 m
30 m
A ball of mass 2.0 kg is thrown vertically upward from the top of a building. The ball’s velocity v is given as a function of time t by the equation v(t) = R - St, where R = 5 m/s and S = 10 m/s2. The positive direction is upward.
What is the ball’s acceleration at time t = 1 s?
-10 m/s2
-5 m/s2
0
5 m/s2
-10 m/s2
he graph above shows velocity as a function of time for a cart moving on a straight, horizontal track.
At which labeled point does the cart have the greatest speed?
A
B
C
D
E
The graph above shows velocity as a function of time for a cart moving on a straight, horizontal track.
At which labeled point does the velocity of the cart change direction?
A
B
C
D
E
A car moves in a straight line along the x-axis. The velocity of the car vx as a function of time t is shown in the graph above. The position x of the car at t=0 is x=0. The average acceleration ax of the car during the interval of 0 to 10s is most nearly
-2.0 m/s2
-0.40 m/s2
+0.40 m/s2
+1.0 m/s2
+2.0 m/s2
A car moves in a straight line along the x-axis. The velocity of the car vx as a function of time t is shown in the graph above. The position x of the car at t=0 is x=0.
The average velocity of the car during the interval of 0 to 10s is most nearly
-1.4 m/s
+0.40 m/s
+1.4 m/s
+1.8 m/s
+4.0 m/s
Cars A and B are moving in opposite directions along a straight road. They pass each other at time t=0. Their velocities v are given as a function of time t in the graph above. The distance between the cars at t=8 s is
zero
24 m
48 m
96 m
192 m
Two stones, represented in the figure above, are thrown from the same height with the same initial speed. Stone A is thrown vertically downward and stone B is thrown horizontally. If the stones are thrown at the same time and air resistance is negligible, which of the following is true?
The two stones will reach the ground at the same time with the same speed.
The two stones will reach the ground at the same time but with different speeds.
Stone A will reach the ground first, but stone B will have the greater speed just before hitting the ground.
Stone A will reach the ground first, but the two stones will have the same speed just before they hit the ground.
Stone A will reach the ground first, and will have the greater speed just before hitting the ground.
An object is moving along a straight line. The object’s velocity as a function of time is shown in the graph above.
During which of the labeled segments on the graph is the object moving but not accelerating?
A
B
C
D
E
An object is moving along a straight line. The object’s velocity as a function of time is shown in the graph above.
The object has a speed of 2 m/s at which of the following times?
1 s only
6 s only
9 s only
4 s and 10 s only
1 s, 6 s, and 9 s
A particle is moving along the y-axis. The particle’s position as a function of time is given by y=αt3−βt+ϕ, where α=1 m/s3, α=1 m/s3, β=4 m/s, and ϕ=3m. What is the particle’s acceleration at time t=3.0s?
6.0 m/s2
9.0 m/s2
18 m/s2
23 m/s2
27 m/s2
An object of mass 10 kg starts from rest at time t = 0 and moves in a straight line. For time t > 0, the object’s velocity v as a function of time t is given by v = 2t + 3t2 , where v is in m/s and t is in seconds.
How far does the object travel during the first 10 s of its motion?
62 m
320 m
283 m
1100 m
1600 m
In an experiment, an object is released from rest from the top of a building. Its speed v is measured as it reaches a point that is a distance d from the point of release. If this distance was doubled, what would the new speed be, assuming air resistance is negligible?
v
2 v
2v
4v
8v
Persons X, Y, and Z walk along a circular path of radius 50 m. Person X walks halfway around the path, Person Y walks 3/4 of the way around the path, and Person Z walks completely around the path. Which of the following correctly lists the walkers in order of the magnitudes of their displacement vectors from the least to the greatest?
X<Y<Z
X<Z<Y
Y<X<C
Y<Z<X
Z<Y<X
A student throws a metal sphere, which follows the path shown above. If air resistance is negligible, which of the following is a correct relationship between the magnitudes of the accelerations aK , aL , and aM at the three points shown?
aK = aL = aM
aK = aL > aM
aK = aM > aL
aK > aL = aM
aK > aM > aL
Student 1 is standing on a cart holding a small stone, while student 2 is standing at rest on the ground, as shown in the figure above. The cart is moving at a constant speed v in the +x-direction, as indicated by the coordinate system shown. Student 1 drops the stone precisely when passing student 2. Which of the following best represents the path of the falling stone relative to student 1 and the path of the falling stone relative to student 2 ?
The position x as a function of time t for an object moving in a straight line is shown in the graph above. Which of the following best describes the object’s speed and direction of motion during the time interval shown?
Decreasing; Positive
Increasing; Positive
Constant; Positive
Decreasing; Negative
Increasing; Negative
A projectile is launched with a speed of 40 m/s at an angle of 30° above the horizontal, as shown in the figure below. The projectile lands on a plateau 3 s later. The height Δy of the plateau is most nearly
15 m
30 m
45 m
60 m
75 m
A block is hung vertically from an ideal spring. The block is pulled down and allowed to oscillate. The position y as a function for time t is shown in the graph above. Which of the following graphs best represents the acceleration a of the block as a function of time?
A 0.50 kg object is attached to a vertical spring of constant k, as shown above. The object is pulled down and released. The object oscillates vertically. If up is the positive direction, the position x of the object as a function of time t is given by the formula
x=βsin(ωt+φ)
, where β = 0.20 m, ω = 4.0 rad/s, and ϕ = π/3 rad
The period of the oscillation for the object is most nearly
4.0 s
3.1 s
2.0 s
1.6 s
1.1 s
The position x of an object is given as a function of time t by the equation x = 8 + 4t - 6t3 , where x is in meters and t is in seconds. What is the maximum positive velocity attained by this object?
4 m/s
8 m/s
18 m/s
36 m/s
There is no maximum positive velocity because the object never moves in the positive direction.
The velocity v in meters per second of an object moving in a straight line is given as a function of time t in seconds by v = 4t3 + 2t. The total distance the object travels between t = 1 s and t = 2 s is
12 m
18 m
24 m
30 m
36 m
A particle of mass m moves counterclockwise around a horizontal circle of radius r, as shown above. The angular speed of the particle is given as a function of time t by ω (t) = bt , where b is a positive constant and t ≥ 0.
Which of the following best describes the acceleration vector for the particle at the moment shown in the diagram?
It is directed toward the left.
It is directed toward the bottom of the page.
It is directed toward the top of the page.
It has components directed toward the right and toward the bottom of the page.
It has components directed toward the left and toward the bottom of the page.
An object moves along a straight line with a velocity v given as a function of time t by the equation v(t)=αt2+βt+γ.
Which of the following expressions represents α(t), the acceleration of the object as a function of time t.
2α
αt+β
2αt+β
αt3/3+βt2/2+γt
3at3+2βt2+γt
An object moves along a straight line with a velocity v
v given as a function of time t
t by the equation v(t)=αt2 + βt+ γ.
Which of the following expressions represents Δx(t), the displacement of the object as a function of time t starting at a time t=0?
2α
αt+β
2αt+β
αt3/3 + βt2/2+γt
3αt3+2βt2+γt
Which of the following statements must be true for a falling object that has been dropped from rest near the surface of Earth?
The derivative of the distance the object falls with respect to time equals 9.8 m/s2
The object falls a vertical distance of 9.8 m during the first second only.
The object falls a vertical distance of 9.8 m during each second.
The speed of the object as it falls is a constant 9.8 m/s.
The speed of the object increases by 9.8 m/s during each second.
