Velocity in accelerated motion

The equation defining acceleration can be rewritten as a model that describes how the velocity changes over time. The result is equation (2.4), which gives the velocity v at time t under the assumption that the acceleration a is constant. In this equation we set Δt = t by assuming the motion starts at t = 0. The initial velocity v0 is the velocity when t = 0. Show Where are <i>t<sub>i</sub></i> and <i>t<sub>f</sub></i>?
(2.4) v= v 0 +at
v  = velocity (m/s)
v0  = initial velocity (m/s)
a  = acceleration (m/s2)
t  = time (s)
Velocity
for constant acceleration
Velocity vs. time for a falling ball To see how equation (2.4) works, consider a ball that is dropped straight down from rest. Starting from rest means that we set vi = 0. If we ignore air friction, gravity causes a constant downward acceleration of −9.8 m/s2. This means that 9.8 m/s is subtracted from the ball's velocity each second. We can calculate that after five seconds of falling the balls velocity is −49 m/s. After ten seconds the velocity is −98 m/s, which is over 200 miles per hour! Notice that in this example, negative acceleration causes the speed to increase, because both acceleration and velocity are in the same direction. The speed increased even as the velocity became more negative!
A ball thrown upwards eventually comes back down again, and equation (2.4) also describes situations where velocity changes direction. Consider throwing a ball straight up with a velocity of +20 m/s. The acceleration of gravity is -9.8 m/s2, therefore velocity changes by −9.8 m/s every second. After two seconds, the ball has a speed of only +0.4 m/s and has nearly stopped!
Velocity vs. time for a ball thrown upwards
After four seconds the ball has a downward or negative velocity of −19.2 m/s. The velocity has changed sign which means the ball has changed direction from moving up to moving down. The term constant acceleration means the same change occurs to the velocity every second, in this case −9.8 m/s2 means a change of −9.8 m/s every second.
Acceleration due to gravity on the Moon is about 1/6 that of the Earth's. Compared to on Earth, a ball thrown upwards on the Moon will take __________ time to return to the surface.
  1. more
  2. the same
  3. less
  4. Not enough information
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