Question

question 20 (1 point) objects a and b both start from rest. they both accelerate at the same rate. however, object a accelerates for twice the time as object b. what is the distance traveled by object a compared to that of object b? the same distance twice as far three times as far four times as far page 20 of 20

Explanation:

Step1: Recall the kinematic equation

The kinematic equation for displacement with constant acceleration starting from rest is \(x = \frac{1}{2}at^{2}\), where \(x\) is the displacement, \(a\) is the acceleration, and \(t\) is the time.

Step2: Express displacements for A and B

Let the time for object B be \(t_{B}=t\), then the time for object A is \(t_{A} = 2t\). The acceleration \(a\) is the same for both.
For object B: \(x_{B}=\frac{1}{2}at^{2}\)
For object A: \(x_{A}=\frac{1}{2}a(2t)^{2}=\frac{1}{2}a\times4t^{2}=4\times(\frac{1}{2}at^{2})\)

Answer:

four times as far