An object moves along the -axis so that its velocity relative to the ground is

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Kinematics · Kinematics

Problem

An object moves along the

x

-axis so that its velocity relative to the ground is

v_{\mathrm{g}}(t)=4t^{2}-3t\,\text{m/s}

. A platform on wheels rolls along the same axis with velocity

u(t)=2t-1\,\text{m/s}

relative to the ground, carrying a video camera that records the object. Which of the following statements about the object’s acceleration

a

as determined by the ground observer and by the camera observer is correct? (a) Both observers measure the same functional form

a(t)=8t-3\,\text{m/s}^2

. (b) The camera observer measures

a(t)=6t-2\,\text{m/s}^2

, which is larger because the platform is speeding up. (c) The two measured accelerations differ by the constant value

2\,\text{m/s}^2

. (d) The camera observer measures

a(t)=8t-1\,\text{m/s}^2

because the platform’s own acceleration adds to that of the object.