In kinematics an object has an initial speed (vi) and undergoes a uniform acceleration (a) for a period of time (t). The distance travelled (s) and the final speed (vf) are determined by vi, a, and t. Since the acceleration is uniform or constant, the average speed is the average of the initial speed and the final speed:

Kinematics


This enables us to derive two more kinematic equations in addition to the definitions of average speed and acceleration:

Kin2






Kin3




  1. From the definitions of average speed and acceleration, derive the two formulas for the distance.
  2. Assume a toy car is travelling at 2 m/s and there is no acceleration. Construct a table showing the distance travelled, the speed, and the acceleration for each second of the first 6 seconds.
  3. What distance is travelled by a train as it is accelerated uniformly from 22 m/s to 44 m/s in 20 s?
  4. A car travelling at 44 m/s is uniformly decelerated to a speed of 22 m/s over an 11-s period. What distance does it travel during this time?
  5. An engineer is to design a runway to accommodate airplanes that must gain a ground speed of 60 m/s before they can take off. The planes accelerate at the rate of 1.5 m/s2. How long will it take the planes to achieve take-off speed? What must be the minimum length of the runway?
  6. A car starting from rest is accelerated at a constant rate of 6.2 m/s2. What distance does the car travel during the first 7.0 s of acceleration?
  7. An airplane starts from rest and undergoes a uniform acceleration of 3.0 m/s2 for 30 s before leaving the ground. What distance does it travel during the 30 seconds?
  8. Assume an airplane starts with an initial speed of zero and is accelerated at 20 m/s2. Construct a table showing the distance traveled, the speed, and acceleration.