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Difficulty: EasyMechanics and Motion

A model electric car accelerates uniformly along a straight track from rest to a speed of 12 m/s12\text{ m/s} in 4 seconds4\text{ seconds}. What is the magnitude of the car's acceleration in meters per second squared (m/s2\text{m/s}^2)?

Answer: 3 m/s^2

Answer

The magnitude of the acceleration is 3 m/s23\text{ m/s}^2.
Acceleration is defined as the change in velocity divided by the time elapsed (a=Δvta = \frac{\Delta v}{t}). Since the car accelerates from 0 m/s0\text{ m/s} to 12 m/s12\text{ m/s} in 4 s4\text{ s}, the acceleration is 12−04=3 m/s2\frac{12 - 0}{4} = 3\text{ m/s}^2.

Step-by-Step Solution

1
Identify the given physical quantities from the problem statement
Initial velocity vi=0 m/sv_i = 0\text{ m/s}, final velocity vf=12 m/sv_f = 12\text{ m/s}, time t=4 st = 4\text{ s}
Establishing known variables is necessary before selecting the appropriate kinematic relationship.
2
Apply the definition of constant linear acceleration: a=ΔvΔt=vf−vita = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}
Formula set up as a=12 m/s−0 m/s4 sa = \frac{12\text{ m/s} - 0\text{ m/s}}{4\text{ s}}
Acceleration represents the rate of change of velocity with respect to time.
3
Perform the division to compute acceleration
a=3 m/s2a = 3\text{ m/s}^2
Dividing 1212 by 44 yields the constant acceleration magnitude.

Key Concept

Uniform Linear Acceleration

Alternative Method

Using the kinematic equation vf=vi+atv_f = v_i + at, substitute 12=0+a(4)12 = 0 + a(4), which simplifies directly to 4a=124a = 12, yielding a=3 m/s2a = 3\text{ m/s}^2.
Estimated Time:45s
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Topics

Mechanics and Motion

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