Kinematics and forces sample question 3

Air drag equals her weight, so her acceleration is zero while she keeps falling at constant speed.

MCAT · Chemical and Physical Foundations · Physics

Kinematics and forces

Kinematics and forces is part of Physics in the MCAT Chemical and Physical Foundations section. The questions below are written in the style of the real test, each with the answer and a worked explanation.

Question types you will see here include projectile motion by components, forces on an inclined plane, static versus kinetic friction thresholds, reading position and velocity and acceleration graphs.

Common traps: using the total launch speed in the vertical equation; assuming speed is zero at the apex (horizontal component persists); swapping sin and cos for the components.

Sample questions

Question 1
A delivery rider on a scooter rounds the same flat curve twice, first at 6.0 m/s and then at 12 m/s. Compared with the first pass, the sideways friction force the road must supply on the second pass is:
- A.
  half as large.
- B.
  the same, because the radius of the curve has not changed.
- C.
  twice as large.
- D.
  four times as large.
Answer: D. four times as large.
Friction supplies the centripetal force mv²/r, which grows with the square of speed: doubling v needs four times the force (D). (C) scales the force linearly with speed; (B) forgets that speed enters the requirement at all; (A) inverts the dependence.
Question 2
A 20 kg cart and a 40 kg cart are released from rest on the same frictionless ramp inclined at 30° to the horizontal. What are their accelerations along the ramp? (g = 10 m/s²)
- A.
  5.0 m/s² for the 20 kg cart and 10 m/s² for the 40 kg cart
- B.
  10 m/s² for both carts
- C.
  8.7 m/s² for both carts
- D.
  5.0 m/s² for both carts
Answer: D. 5.0 m/s² for both carts
The force along the ramp is mg sin θ, and dividing by m leaves a = g sin 30° = 5.0 m/s² whatever the mass (D). (A) lets acceleration grow with mass, forgetting that the larger force acts on a larger mass; (C) uses cos θ instead of sin θ; (B) ignores the incline and uses free-fall acceleration.
Question 3
A skydiver falling belly-down has reached terminal speed. Which statement about her motion is correct?
- A.
  Air drag equals her weight, so her acceleration is zero while she keeps falling at constant speed.
- B.
  Her acceleration is g, because gravity is still pulling on her.
- C.
  Air drag is larger than her weight, which is why her speed stops increasing.
- D.
  Her velocity and her acceleration are both zero.
Answer: A. Air drag equals her weight, so her acceleration is zero while she keeps falling at constant speed.
At terminal speed the upward drag has grown to match her weight, so the net force and acceleration are zero and her velocity stays constant and downward (A). (B) ignores drag; (C) would make her slow down; (D) confuses zero acceleration with zero velocity.
Question 4
A 10 kg box on a level floor is pulled horizontally with a 60 N force. The coefficient of kinetic friction is 0.3. Using g = 10 m/s², what is the box's acceleration?
- A.
  3 m/s²
- B.
  5.7 m/s²
- C.
  6 m/s²
- D.
  9 m/s²
Answer: A. 3 m/s²
Friction is μmg = 0.3(10)(10) = 30 N, so the net force is 60 − 30 = 30 N and a = F_net/m = 3 m/s². Ignoring friction gives F/m = 6 m/s².
Question 5
Blood moving at 1.0 m/s follows the aortic arch, which has a radius of curvature of 0.05 m. The centripetal acceleration of the blood is:
- A.
  0.05 m/s²
- B.
  2.0 m/s²
- C.
  20 m/s²
- D.
  200 m/s²
Answer: C. 20 m/s²
a = v²/r = (1.0 m/s)² / 0.05 m = 20 m/s², about twice g, which is why the aortic wall must exert a substantial inward force on the blood rounding the arch. The value 0.05 m/s² is v × r, 2.0 m/s² uses r = 0.5 m, and 200 m/s² uses r = 0.005 m.

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