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Difficulty: EasySpeed, Velocity, and Acceleration

A hydraulic press ram must reach a downward operating velocity of 0.8 m/s0.8 \text{ m/s} starting from rest. If the hydraulic system is calibrated to accelerate the ram at a constant rate of 0.2 m/s20.2 \text{ m/s}^2, how many seconds will it take for the ram to reach its target velocity?

  1. A
    0.16 s0.16 \text{ s}
  2. B
    0.25 s0.25 \text{ s}
  3. 4.0 s4.0 \text{ s}Answer
  4. D
    40.0 s40.0 \text{ s}

Answer

It will take 4.0 s4.0 \text{ s} for the hydraulic press ram to reach the target velocity.
The time required to reach a specific velocity from rest is calculated by dividing the target velocity by the constant acceleration (t=vat = \frac{v}{a}). Dividing 0.8 m/s0.8 \text{ m/s} by 0.2 m/s20.2 \text{ m/s}^2 results exactly in 4.0 seconds4.0 \text{ seconds}.

Step-by-Step Solution

1
Identify the known kinematic variables from the scenario.
Initial velocity is 0 m/s0 \text{ m/s}, final velocity is 0.8 m/s0.8 \text{ m/s}, and acceleration is 0.2 m/s20.2 \text{ m/s}^2.
Organizing the known values determines which rate formula must be applied.
2
Rearrange the acceleration formula to solve for time.
The formula a=Δvta = \frac{\Delta v}{t} becomes t=Δvat = \frac{\Delta v}{a}.
To isolate the unknown variable (time) from the standard acceleration equation.
3
Calculate the final elapsed time.
0.8÷0.2=4.0 seconds0.8 \div 0.2 = 4.0 \text{ seconds}.
Executing the division yields the time required to reach the target velocity.

Key Concept

Kinematic Rate Equations (Solving for Time)
Estimated Time:45s
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Topics

Speed, Velocity, and Acceleration

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