Each of four particles moves along an x axis.Their coordinates (in meters)as functions of time (in seconds)are given by
Which of these particles have constant acceleration?
A)All four
B)Only 1 and 2
C)Only 2 and 3
D)Only 3 and 4
E)None of them

Question

Each of four particles moves along an x axis.Their coordinates (in meters)as functions of time (in seconds)are given by  
Which of these particles have constant acceleration?
A)All four 
B)Only 1 and 2 
C)Only 2 and 3 
D)Only 3 and 4 
E)None of them

Quizplus · Accepted Answer

We can determine the acceleration of each particle by taking the second derivative of its position function with respect to time.

Particle 1: a(t) = 0.2
Particle 2: a(t) = -0.3
Particle 3: a(t) = 0
Particle 4: a(t) = -0.1

Particles with constant acceleration would have a constant second derivative, which means their acceleration would not change over time. Therefore, the only particles with constant acceleration are those with a(t) = 0 or a constant non-zero value.

Particles 2 and 3 have constant acceleration, while particles 1 and 4 do not. Therefore, the answer is D, only particles 3 and 4 have constant acceleration.

Each of Four Particles Moves Along an X Axis