The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to 6 s. What is the average speed of the particle over the intervals in (a) and (b)?
Distance travelled by the particle = Area under the given graph.
= (1/2) × (10 - 0) × (12 - 0)
= 60 m
Let s1 and s2 be the distances covered by the particle between time t = 2 s to 5 s and t = 5s to 6 s respectively.
Total distance (s) covered by the particle in time t = 2 s to 6 s is,
s = s1 + s2 … (i) For distance s1 ,
Let u1be the velocity of the particle after 2 s, and a1 be the acceleration of the particle in t = 0 to t = 5s.
The particle undergoes uniform acceleration in the first 5 seconds.
Therefore, using first equation of motion v = u+at, we have
12 = 0 + a1 × 5
i.e., a1 = 12/5 = 2.4 m/s2
Again, using the first equation of motion, we have
v = u + at
= 0 + 2.4 × 2
= 4.8 m/s
Distance travelled by the particle between time 2 s and 5 s i.e., in 3 s
s1 = u1t + (1/2) a1t2
= 4.8 × 3 + (1/2) × 2.4 × (3)2
= 25.2 m ...(ii)
For distance s2:
Let a2 be the acceleration of the particle between time t = 5 s and t = 10 s.
Using first equation of motion,
v = u + at
0 = 12 + a2 × 5
a2 = -12 / 5 = - 2.4 ms-2
Distance travelled by the particle in 1s (i.e., between t = 5 s and t = 6 s),
s2 = u2 t + (1/2)a2t2
= 12 × 1 + (1/2) (-2.4) × (1)2
= 12 - 1.2 = 10.8 m ...(iii)
Now, from equations (i), (ii) and (iii), we have
s = 25.2 + 10.8 = 36 m
∴ Average speed = 36 / 4 = 9 m/s
Is absolute rest or absolute motion possible?
Absolute rest and absolute motion is not possible because there is no point in the universe which is at rest and can be taken as point of reference. The planet Earth is in continuous motion.
What is the most essential thing to study the motion of a body?
The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion.