A body moving with uniform acceleration is having
velocity 2 m/s and 8 m/s at t = 1s and t = 45
respectively. Then average velocity of particle in the
time interval t = 1 s to t = 4 s is
(1) 2 m/s
(3) 5/3 m/s
(4) 5 m/s
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answer : option (4) 5m/s
explanation : A body moving with uniform acceleration (let a) is having 2m/s at t = 1s and 8m/s at t = 4s [ you wrote 45 by mistake ]
so, initial velocity , u = 2m/s
final velocity , v = 8m/s
time duration, t = 4s - 1s = 3s
using formula, v = u + at
or, 8m/s = 2m/s + a × 3s
or, 6m/s = 3s × a
or, a = 2m/s²
hence, acceleration of body , a = 2m/s²
now, total displacement covered by body in time intervals t = 1s to 4s.
s = ut + 1/2 at²
= 2 × 3 + 1/2 × 2 × 3²
= 6 + 9 = 15m
now average velocity = total displacement/total time taken
= 15m/3s
= 5m/s.
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