Warm-Up Exercise 1

Due 2:00 pm, Tuesday, January 6

If the acceleration of an object is in the opposite direction of its velocity, then
the object is speeding up,
the object is slowing down, or
the object may be speeding up or slowing down, depending on the direction of its velocity.

If I throw a ball straight up into the air, we say the ball is a "freely falling object"
on its way up,
on its way back down, or
both on its way up and on its way back down.

A ball tossed vertically upward rises, reaches its highest point, and then falls back to its starting point. During this time, the acceleration of the ball is always
in the direction of motion,
opposite its velocity,
directed downward, or
directed upward.

Ralph asked me a question the other day. Consider a car accelerating forward. Its acceleration is 1.8 m/s². During the first second, the car accelerates from 0 to 1.8 m/s. Ralph thought that since the velocity at the end of the first second is 1.8 m/s, the car would travel 1.8 m during that first second. But someone told him that the answer is actually 0.9 m. Can you help Ralph understand why? Don't just say, "Because the formula in the book says so."
The answer would be 1.8 m if that were the velocity of the car during the entire second. But that was its speed only at the end of the second. Since it started from rest (v=0), the average velocity during the first second is (0+1.8)/2=0.9 m/s. So the distance traveled is 0.9 m. That's why there is a factor 1/2 in the formula (1/2)at^2. We calculate the distance from the average velocity over the time interval.