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Physics Final Exam Practice Problems

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  • Identify the vectors among acceleration, velocity, speed, displacement, and mass.
    Acceleration, velocity, and displacement are vectors; speed and mass are scalars.
  • How many seconds are in a year?
    Approximately 3.15 × 10^7 seconds in a year.
  • When are two trains moving at the same speed given their position vs. time graphs?
    At the time t_c where the slopes of their position-time graphs are equal.
  • Final speed of a dragster starting from rest with acceleration a=20 m/s² for 5 seconds?
    Final speed \(v=at=20 \times 5=100\,m/s\).
  • Final speed of a car accelerating with a = ct³ for time T?
    Final speed \(v=\int_0^T ct^3 dt=\frac{cT^4}{4}\).
  • What does the velocity vs. time graph look like for a wind-up car traveling at almost constant velocity?
    A horizontal line indicating constant velocity after negligible acceleration time.
  • How many meters is a light-year?
    Approximately \(9.46 \times 10^{15}\,m\).
  • Can two nonzero vectors of unequal magnitude sum to zero?
    False. Only vectors of equal magnitude and opposite direction can sum to zero.
  • Time to reach maximum height for a projectile fired straight up at speed v₀?
    \(t=\frac{v_0}{g}\) where g is acceleration due to gravity.
  • Time for a ball dropped from height h to hit the ground (ignore air resistance)?
    \(t=\sqrt{\frac{2h}{g}}\).
  • Speed of a ball when it hits the ground after being dropped from height h?
    \(v=\sqrt{2gh}\).
  • Speed of a ball thrown straight up at speed v₀ from height h when it hits the ground?
    \(v=\sqrt{v_0^2 + 2gh}\).
  • Distance from start after walking 10 km east, 20 km north, then 5 km west?
    Resultant displacement is approximately \(\sqrt{(10-5)^2 + 20^2} = 20.6\,km\).
  • Average velocity when traveling 100 km east in 1 hour, then 100 km south in 2 hours?
    Average velocity magnitude is \(\frac{\sqrt{100^2 + 100^2}}{3} \approx 47.1\,km/h\).
  • Range of a projectile launched at speed v₀ and angle θ?
    \(R=\frac{v_0^2 \sin 2\theta}{g}\).
  • Height reached by a projectile launched at speed v₀ and angle θ?
    \(h=\frac{v_0^2 \sin^2 \theta}{2g}\).
  • Is a car driving in a circle at constant speed accelerating?
    Yes, it has centripetal acceleration directed toward the center of the circle.
  • Velocity of a particle with position vector r = 10 j + 20 t i - 4.9 t² j at t=0?
    Velocity at t=0 is \(\vec{v} = 20 \hat{i}\).
  • Acceleration of the same particle at t=5 s?
    Acceleration is constant \(\vec{a} = -9.8 \hat{j}\).
  • Angle to point yourself to swim straight across a river flowing east at speed v_r with swimming speed v_s?
    Point at angle \(\theta = \arcsin \left( \frac{v_r}{v_s} \right)\) upstream.