Motion in a straight line:
VELOCITY
Rate of change of displacement (or position) with respect to time is called as velocity. Thus v=ds/dt
ACCELERATION
The rate of change of velocity with respect to time is called as acceleration. Therefore at time t
NOTE : The direction of acceleration is in direction of velocity or is opposite to it. When direction of acceleration is opposite to direction of velocity then it is called as retardation. Retardation means the negative acceleration.
Example 1 A particle which is moving in straight line covers s meter in t sec. If s = 3t+t3 then find out values for following:
(i) Acceleration after 2 sec.
(ii) Time when velocity is 51 m/s.
(iii) Distance travelled in 3rd sec.
Solution:
Acceleration after 2 seconds = 6 x 2 = 12 m/s.
velocity = ds/dt =51 m/s
After 4 seconds velocity is 51 m/s
s = 3t+t3
Distance after 3 seconds = 3 x 3+33 =36 m
Distance after 2 seconds = 3 x 2 + 23 =14m
Distance travelled in 3rd seconds = 36 - 14 = 22 m
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