Question

a particle starts with an angular acceleration 2 rad/sec square. it moves 100 rad in random interval of 5 sec. find out the time at which random interval starts

Answer 1

Hey mate,

◆ Answer- 7.5 s

◆ Explanation-
# Given -
t2 - t1 = 5 s ...(3)
θ2 - θ1 = 100 rad
α = 2 rad/s^2

# Solution-
Applying Newton's kinematic eqn for rotational motion-
θ1 = 1/2 αt1^2 ...(1)
θ2 = 1/2 αt2^2 ...(2)

Subtracting,
θ2 - θ1 = 1/2 αt2^2 - 1/2 αt1^2
θ2 - θ1 = 1/2 α(t2^2 - t1^2)
θ2 - θ1 = 1/2 α(t2 - t1)(t2 + t1)
100 = 1/2 2(5)(t2 + t1)
t2 + t1 = 20 ...(4)

Solving (3) and (4), we get
t1 = 7.5 s
t2 = 12.5 s

Therefore, we can say that random interval started at 7.5 s.

Hope that is useful...