Use the equation for the motion of an accelerating object to answer the question.

x=x0+v0t+12at2

Which equation could describe the motion of an object starting at x=0 with a starting speed of 10 m/s and an acceleration of 3 m/s2?

(1 point)
Responses

x=1.5+10t
x is equal to 1 point 5 plus 10 t

x=10t+1.5t2
x is equal to 10 t plus 1 point 5 t squared

x=3+5t2

1 answer

To find the equation that describes the motion of the object, we can use the formula:

x=x0+v0t+12at2

Given:

  • Starting position x0=0
  • Starting speed v0=10,m/s
  • Acceleration a=3,m/s2

Substituting these values into the equation:

x=0+10t+12(3)t2

This simplifies to:

x=10t+32t2

Now, 32t2=1.5t2, so we can rewrite it as:

x=10t+1.5t2

Looking at the response options:

  1. x = 1.5 + 10t (Incorrect, doesn't match)
  2. x = 10t + 1.5t^2 (Correct, matches the derived equation)
  3. x = 3 + 5t^2 (Incorrect, doesn't match)

The correct response is:

x = 10t + 1.5t^2