MCQ Unit 1: Kinematics

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?

• v_o sin θ - gt

• v_o cos θ - gt

• $\sqrt{v_o^2\cos^2θ+(v_o\sinθ-gt)^2}$

• $\sqrt{(v_o\cosθ-gt)^2+v_o^2\ \sin^2θ}$

• $\sqrt{(v_o\cosθ-gt)^2+(v_o\sinθ-gt)^2}$

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