Examkin

Question

Difficulty: MediumSpeed, Velocity, and Acceleration

A maglev transit pod enters a straight acceleration zone with an initial velocity of 20 m/s20 \text{ m/s}. The pod's linear induction motors apply a constant acceleration of 5 m/s25 \text{ m/s}^2 for exactly 0.1 minutes0.1 \text{ minutes}. What is the pod's final velocity at the end of this time period?

  1. A
    20.5 m/s20.5 \text{ m/s}
  2. B
    30 m/s30 \text{ m/s}
  3. 50 m/s50 \text{ m/s}Answer
  4. D
    70 m/s70 \text{ m/s}

Answer

The correct answer is 50 m/s50 \text{ m/s}.
The final velocity is found by first converting the given time to standard units (0.1 minutes=6 seconds0.1 \text{ minutes} = 6 \text{ seconds}). Next, determine the total velocity gained by multiplying acceleration by time (5 m/s2×6 s=30 m/s5 \text{ m/s}^2 \times 6 \text{ s} = 30 \text{ m/s}). Finally, add this gained velocity to the initial velocity of 20 m/s20 \text{ m/s} to get a final velocity of 50 m/s50 \text{ m/s}.

Step-by-Step Solution

1
Convert the given time from minutes to seconds.
0.1 minutes×60 seconds/minute=6 seconds0.1 \text{ minutes} \times 60 \text{ seconds/minute} = 6 \text{ seconds}
Acceleration is given in m/s2\text{m/s}^2, so time must be in seconds to match units.
2
Calculate the total change in velocity (Δv\Delta v) during the acceleration period.
Δv=a×t=5 m/s2×6 s=30 m/s\Delta v = a \times t = 5 \text{ m/s}^2 \times 6 \text{ s} = 30 \text{ m/s}
This determines how much speed the pod gained.
3
Add the change in velocity to the initial velocity to find the final velocity.
vf=vi+Δv=20 m/s+30 m/s=50 m/sv_f = v_i + \Delta v = 20 \text{ m/s} + 30 \text{ m/s} = 50 \text{ m/s}
The final velocity is the starting velocity plus whatever velocity was gained.

Key Concept

Applying kinematic equations for constant acceleration (vf=vi+atv_f = v_i + at) with required unit conversions.
Rate this question

Topics

Speed, Velocity, and Acceleration

More questions from this topic