Kinematics, Newton's Laws and Energy
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Part 1 of 1
1. Motion under constant acceleration
A sprinter covering 100 m in 10 s averages 10 m/s. That single number hides everything interesting, because the sprinter did not travel at 10 m/s at any particular moment. Average speed is total distance over total time and nothing more.
When acceleration is constant, four equations connect initial velocity u, final velocity v, acceleration a, displacement s and time t. The two you will use most are v = u + at and s = ut + at squared over 2.
Distance and displacement are not the same. Distance is the ground covered, displacement is the straight line from start to finish with a direction attached. Walk 5 m forward and 5 m back and you have covered 10 m of distance and zero displacement. Questions that mention returning to the starting point are usually testing exactly this.
Worked example
A car starts from rest and accelerates at 2 m/s squared for 5 s. Its final velocity is v = 0 + 2 times 5 = 10 m/s. The distance covered is s = 0 + half times 2 times 25 = 25 m. Note the average velocity over that time is 5 m/s, and 5 times 5 = 25 m, which is a useful way to check the answer.
1.An object moving at constant velocity has zero acceleration.
2.Distance and displacement always have the same magnitude.
3.To convert a speed in km/h into m/s you divide by 3.6.
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