Math Skills
Calculating Acceleration
A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball?
Read and Understand
What information are you given?
Time = 2 s
Starting velocity = 0 m/s
Ending velocity = 6 m/s
Plan and Solve
What unknown are you trying to calculate?
Acceleration = ?
What formula contains the given quantities and the unknown?
Replace each variable with its known value.
Look Back and Check
Is your answer reasonable?
Objects in free fall accelerate at a rate of 9.8 m/s2. The ramp is not very steep. An acceleration of 3 m/s2 seems reasonable.
Math Practice
A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its acceleration?
An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s2. What is its change in velocity during this time?
A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water?
A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boy's hand?
Graphs of Accelerated Motion
You can use a graph to calculate acceleration. For example, consider a downhill skier who is moving in a straight line. After traveling down the hill for 1 second, the skier's speed is 4 meters per second. In the next second the speed increases by an additional 4 meters per second, so the skier's acceleration is 4 m/s2. Figure 16 is a graph of the skier's speed. 
The slope of a speed-time graph is acceleration. This slope is change in speed divided by change in time.
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